A criterion of weak compactness for operators on subspaces of Orlicz spaces

The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$

A subspace $H$ of a rearrangement invariant space $X$ on $[0,1]$ is strongly embedded in $X$ if, in $H$, convergence in $X$-norm is equivalent to convergence in measure. We obtain necessary and sufficient conditions on an Orlicz function $M$, under which the unit ball of an arbitrary strongly embedded subspace in the Orlicz space $L_M$ has equi-absolutely continuous norms in $L_M$.

Musielak-Orlicz Spaces that are Isomorphic to Subspaces of L_1

In this note we prove that $\frac{1}{n!} \sum_π (\sum_{i=1}^n |x_i a_{i,π(i)} |^2)^{1/2}$ is equivalent to a Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain the embedding of 2-concave Musielak-Orlicz spaces into L_1.

Representations of the Orlicz Figa-Talamanca Herz Algebras and Spectral subspaces

Let G be a locally compact group. In this note, we characterise non-degenerate *-representations of A_Φ(G) and B_Φ(G). We also study spectral subspaces associated to a non-degenerate Banach space representation of A_Φ(G).

Characterization of the lack of compactness of $H^2_{rad}(\R^4)$ into the Orlicz space

This paper is devoted to the description of the lack of compactness of the Sobolev space $H^2_{rad}(\R^4)$ in the Orlicz space $\mathcal{L}(\R^4)$. The approach that we adopt to establish this characterization is in the spirit of the one adopted in the case of $H^1_{rad}(\R^2)$ into the Orlicz space $\mathcal{L}(\R^2)$ in \cite{Bahouri}.

由零均值函数的独立副本张成的Orlicz空间子空间

On subspaces of Orlicz spaces spanned by independent copies of a mean zero function

本文研究由零均值函数的独立副本张成的Orlicz空间子空间，刻画其强嵌入性及单位球范数等度连续性，并给出当且仅当条件（指数不等式）成立的一类广泛空间。

用 Orlicz 函数表述的 $L_1$ 空间中的弱紧性准则

Weak compactness criteria in $L_1$ space in terms of Orlicz function

本文研究 $L_1$ 空间中弱紧性的 Orlicz 函数刻画，直接证明 K.M. Chong 与 De la Vallée Poussin 准则在 $L_1(0,1)$ 中等价，并讨论其在 $L_1(0,\infty)$ 中的情形。

Description of the lack of compactness in Orlicz spaces and applications

In this paper, we investigate the lack of compactness of the Sobolev embedding of $H^1(\R^2)$ into the Orlicz space $L^{ϕ_p}(\R^2)$ associated to the function $ϕ_p$ defined by $ϕ_p(s):={\rm{e}^{s^2}}-\Sum_{k=0}^{p-1} \frac{s^{2k}}{k!}\cdot$ We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm $\|.\|_{L^{ϕ_p}}$ plays a crucial role. This study includes issues of global existence, scattering and qualitative study.

Continuity and Bargmann mapping properties of quasi-Banach Orlicz modulation spaces

We deduce continuity, compactness and invariance properties for quasi-Banach Orlicz modulation spaces. We characterize such spaces in terms of Gabor expansions and by their images under the Bargmann transform.

One-complemented subspaces of real sequence spaces

Characterizations are given for 1-complemented hyperplanes of strictly monotone real Lorentz spaces and 1-complemented finite codimensional subspaces (which contain at least one basis element) of real Orlicz spaces equipped with either Luxemburg or Orlicz norm.

Multiplication and composition operators between two Orlicz spaces

In this paper we consider composition operator $C_φ generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we investigate boundedness, compactness and essential norm of multiplication and composition operators in term of properties of the mapping $φ$, the function $u$ and the measure space $(X, Σ, μ)$.

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^Ψ$ and Bergman-Orlicz ${\mathfrak B}^Ψ$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^Ψ$ but not on ${\mathfrak B}^Ψ$.

Bergman-Orlicz 空间上复合算子的紧线性组合

Compact linear combination of composition operators on Bergman-Orlicz spaces

本文在 Orlicz 函数增长假设下，利用 Julia-Caratheodory 型函数论与 Carleson 型测度技巧，完全刻画了 Bergman-Orlicz 空间上复合算子有限线性组合的紧性。

Orlicz spaces associated to a quasi-Banach function space. Applications to vector measures and interpolation

We characterize the relatively compact subsets of $L^1\left(\| m \| \right),$ the quasi-Banach function space associated to the semivariation of a given vector measure $m$ showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak compactness that appears in the classic setting of Lebesgue spaces remains almost invariant in this new context of the Choquet integration. Also we present a de la Vallée-Poussin type theorem in the context of these spaces $L^1\left(\|m\|\right)$ that allows us to locate each compact…

Compact composition operators on $H^2$ and Hardy-Orlicz spaces

We compare the compactness of composition operators on $H^2$ and on Orlicz-Hardy spaces $H^Ψ$. We show in particular that exists an Orlicz function $Ψ$ such that $H^{3+\eps} \subseteq H^Ψ\subseteq H^3$ for every $\eps >0$, and a composition operator $C_ϕ$ which is compact on $H^3$ and on $H^{3+\eps}$, but not compact on $H^Ψ$.

线性子空间的最佳 Musielak-Orlicz 逼近

The best Musielak-Orlicz approximation by linear subspaces

本文研究 Musielak-Orlicz 空间中的最佳模逼近，通过 Orlicz 函数原点附近的几何分类，在最小假设下建立存在性结果，并利用单侧导数刻画极小元，最终给出唯一性准则，包括 Haar 型定理和高维空间中的刻画。

Compact composition operators on Bergman-Orlicz spaces

We construct an analytic self-map $ϕ$ of the unit disk and an Orlicz function $Ψ$ for which the composition operator of symbol $ϕ$ is compact on the Hardy-Orlicz space $H^Ψ$, but not compact on the Bergman-Orlicz space ${\mathfrak B}^Ψ$. For that, we first prove a Carleson embedding theorem, and then characterize the compactness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2.

Orlicz序列空间的遍历性

The ergodicity of Orlicz sequence spaces

本文证明非希尔伯特可分Orlicz序列空间具有遍历性，含连续统多个两两不同构子空间，同时推导Kalton-Peck构造的相关扭曲希尔伯特空间要么为希尔伯特空间要么具有遍历性。

Fractional Orlicz-Sobolev embeddings

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order $s\in (0,1)$, and higher-order spaces are considered. Related Hardy type inequalities are proposed as well. An extension theorem is proved, that enables us to derive embeddings for spaces defined in Lipschitz domains. Necessary and sufficient conditions for the compactness of fractional Orlicz-Sobolev…

Contractive projections in Orlicz sequence spaces

We characterize norm one complemented subspaces of Orlicz sequence spaces $\ell_M$ equipped with either Luxemburg or Orlicz norm, provided that the Orlicz function $M$ is sufficiently smooth and sufficiently different from the square function. This paper concentrates on the more difficult real case, the complex case follows from previously known results.

On the lack of compactness in the 2D critical Sobolev embedding

This paper is devoted to the description of the lack of compactness of $H^1_{rad}(\R^2)$ in the Orlicz space. Our result is expressed in terms of the concentration-type examples derived by P. -L. Lions. The approach that we adopt to establish this characterization is completely different from the methods used in the study of the lack of compactness of Sobolev embedding in Lebesgue spaces and take into account the variational aspect of Orlicz spaces. We also investigate the feature of the solutions of non linear wave equation with exponential growth, where the Orlicz norm plays a decisive role.

Some isomorphically polyhedral Orlicz sequence spaces

A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is $c_0$-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of $c_0$. In this paper, we show that the Orlicz sequence space $h_M$ is isomorphic to a polyhedral Banach space if $\lim_{t\to 0}M(Kt)/M(t) = \infty$ for some $K < \infty$. We also construct an Orlicz sequence space $h_M$ which is $c_0$-saturated, but which is not isomorphic to any polyhedral Banach space. This shows that being $c_0$…

Embedding Orlicz Sequence Spaces into $C(α)$

Let $M$ be a non-degenerate Orlicz function such that there exist $\ep > 0$ and $0 < s < 1$ with $\su M(\ep s^i)/M(s^i) < \infty$. It is shown that the Orlicz sequence space $h_M$ is isomorphic to a subspace of $C(\om^\om)$. It is also shown that for any non-degenerate Orlicz function $M$, $h_M$ does not embed into $C(\al)$ for any $\al < \om^\om$.

Isomorphic copies of $l^\infty$ in Cesàro-Orlicz function spaces

We characterize Cesàro-Orlicz function spaces $Ces_φ$ containing isomorphic copy of $l^\infty$. We also describe the subspaces $(Ces_φ)_a$ of all order continuous elements of $Ces_φ$. Finally, we study the monotonicity structure of the spaces $Ces_φ$ and $(Ces_φ)_a$.

Schauder-Orlicz 分解、$\ell_Φ$-分解与伪 Daugavet 性质

Schauder-Orlicz decompositions, $\ell_Φ$-decompositions and pseudo-Daugavet property

本文推广了Banach空间的$\ell_p$-分解概念，提出$\ell_Φ$-分解与Schauder-Orlicz分解，并证明在具有伪Daugavet性质的空间中不存在包含有限维子空间的此类分解。

Closed subspaces and some basic topological properties of noncommutative Orlicz spaces

In this paper, we study the noncommutative Orlicz space $L_φ(\widetilde{\mathcal{M}},τ)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\mathcal{M}$ is a von Neumann algebra, and $φ$ is an Orlicz function. As a modular space, the space $L_φ(\widetilde{\mathcal{M}},τ)$ possesses the Fatou property, and consequently, it is a Banach space. In addition, a new description of the subspace $E_φ(\widetilde{\mathcal{M}},τ)=\overline{\mathcal{M}\bigcap L_φ(\widetilde{\mathcal{M}},τ)}$ in $L_φ(\widetilde{\mathcal{M}},τ)$, which is closed under the norm topology and dense under the…

Orlicz-Lorentz空间的Köthe对偶研究

On Köthe duals of Orlicz-Lorentz spaces

本文研究Orlicz-Lorentz空间的Köthe对偶空间$\u200b\mathcal{M}_{φ,w}$的性质，刻画其序连续子空间、可分性与Radon-Nikodým性质，给出空间比较关系，并应用于M-嵌入子空间与保范延拓问题。

Basic topological and geometric properties of Cesàro--Orlicz spaces

Necessary and sufficient conditions under which the Cesàro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro--Orlicz spaces $\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\cfi$ are given.

Convolution Properties of Orlicz Spaces on hypergroups

In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(Φ_1, Φ_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the convolution $f\ast g$ to exist a.e., where $f$ and $g$ are arbitrary elements of Orlicz spaces $L^{Φ_1}(K)$ and $L^{Φ_2}(K)$, respectively. As an application, we present some equivalent conditions for compactness of a compactly generated locally compact abelian group. Moreover, we also characterize compact convolution operators from $L^1_w(K)$ into $L^Φ_w(K)$ for a…

Orlicz-Sobolev nematic elastomers

We extend the existence theorems in [Barchiesi, Henao \& Mora-Corral; ARMA 224], for models of nematic elastomers and magnetoelasticity, to a larger class in the scale of Orlicz spaces. These models consider both an elastic term where a polyconvex energy density is composed with an unknown state variable defined in the deformed configuration, and a functional corresponding to the nematic energy (or the exchange and magnetostatic energies in magnetoelasticity) where the energy density is integrated over the deformed configuration. In order to obtain the desired compactness and lower semicontinu…

A threshold phenomenon for embeddings of $H^m_0$ into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.

Geometry of Orlicz spaces equipped with norms generated by some lattice norms in $\mathbb{R}^{2}$

In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$) studied in [10-11], [14-15] and [20]. Criteria for strict monotonicity, lower and upper local uniform monotonicities and uniform monotonicities of Orlicz spaces and their subspaces of order continuous elements, equipped with these norms, are given in terms of the generating Orlicz functions, and the lattice norm in $\mathbb{R}^{2}$. The problems of strict convexi…

$M$-ideal properties in Orlicz-Lorentz spaces

We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $Λ_{φ,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, and we show that the norm of a singular functional is the same regardless of the norm in the space, while the formulas of the norm of general functionals are different for the Luxemburg and Orlicz norm. The relationship between equivalent definitions of the modular $P_{φ,w}$ generating the dual space to Orlicz-Lorentz space is discussed in order to co…

1-complemented subspaces of spaces with 1-unconditional bases

We prove that if $X$ is a complex strictly monotone sequence space with $1$-unconditional basis, $Y \subseteq X$ has no bands isometric to $\ell_2^2$ and $Y$ is the range of norm-one projection from $X$, then $Y$ is a closed linear span a family of mutually disjoint vectors in $X$. We completely characterize $1$-complemented subspaces and norm-one projections in complex spaces $\ell_p(\ell_q)$ for $1 \leq p, q < \infty$. Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are $1$-complemented in (real or complex) Orlicz or …

The Dirichlet Problem for Orlicz-Sobolev mappings between metric space

In this paper, we solve the Dirichlet problem for Orlicz-Sobolev maps between singular metric spaces that extends the corresponding result of Guo et al. [arXiv 2021]. As an intermediate step, we develop a version of Rellich-Kondrachov compactness theorem for Orlicz-Sobolev mappings between metric spaces that extends a previous result of Guo and Wenger [Comm. Anal. Geom. 2020]. Another crucial ingredient is an Orlicz-Sobolev extension of the trace theory for metric valued Sobolev maps developed by Korevaar and Schoen [Comm. Anal. Geom. 1993].

非交换 Orlicz 空间上的乘子

Multipliers on Noncommutative Orlicz Spaces

本文研究非交换 Orlicz 空间间乘法算子的存在判据，证明其涵盖已有结果，并比较其与 $L^p$ 空间理论的差异及算子紧性。

Orlicz-Lorentz空间分析的新结果

New Results in Analysis of Orlicz-Lorentz spaces

本文研究Orlicz-Lorentz空间中非线性子集的空间性、极大空间性及可线性性，刻画不同权重下的包含算子，推广了Orlicz和Lorentz空间的已知结果。

函数空间中的无条件基序列及其在 Orlicz 空间中的应用

Unconditional basic sequences in function spaces with applications to Orlicz spaces

本文研究了函数空间 $\bf{L}$ 的无条件基序列，提出了一个二分法条件，使得其互补子空间的无条件基要么等价于 $\ell_2$ 的单位向量系，要么具有不相交支撑的子基，并据此分类了对称基序列，应用于 Orlicz 空间。

局部紧群上Orlicz与混合范数Orlicz空间中非衰减信号的相关采样

Relevant sampling of non-decaying signals in Orlicz and mixed-norm Orlicz spaces defined on a locally compact group

本文针对局部紧群上非衰减信号，在加权Orlicz及混合范数Orlicz空间中建立确定性、平均及随机采样定理，并应用于平移不变空间与Orlicz调制空间。

Embeddings of Orlicz-Lorentz spaces into $L_1$

In this article, we show that Orlicz-Lorentz spaces $\ell^n_{M,a}$, $n\in\mathbb N$ with Orlicz function $M$ and weight sequence $a$ are uniformly isomorphic to subspaces of $L_1$ if the norm $\|\cdot\|_{M,a}$ satisfies certain Hardy-type inequalities. This includes the embedding of some Lorentz spaces $d^n(a,p)$. Our approach is based on combinatorial averaging techniques and we prove a new result of independent interest that relates suitable averages with Orlicz-Lorentz norms.

Orlicz-Lorentz空间中的Daugavet性质与直径二性质

Daugavet and diameter two properties in Orlicz-Lorentz spaces

本文研究了配备Luxemburg范数的Orlicz-Lorentz空间的直径二性质与Daugavet性质，通过Orlicz函数的$Δ_2$-条件刻画了相关性质及其Köthe对偶空间的特征，并揭示了其与$L_1$等距同构的条件。

Orlicz-BMO交换子在Orlicz-Hardy型空间上的端点有界性

Endpoint boundedness of Orlicz-BMO commutators on Orlicz-Hardy type spaces

本文研究次线性算子与Orlicz-BMO函数生成的交换子在Orlicz-Hardy型空间上的端点有界性，证明了两类有界性结果，指出仅Bochner-Riesz平均算子对应的交换子满足特定端点有界性并给出反例。

Orlicz property of operator spaces and eigenvalue estimates

As is well known absolute convergence and unconditional convergence for series are equivalent only in finite dimensional Banach spaces. Replacing the classical notion of absolutely summing operators by the notion of 1 summing operators \[ \summ_k || Tx_k || \leq c || \summ_k e_k \otimes x_k ||_{\ell_1\otimes_{min}E}\] in the category of operator spaces, it turns out that there are quite different interesting examples of 1 summing operator spaces. Moreover, the eigenvalues of a composition $TS$ decreases of order $n^{\frac{1}{q}}$ for all operators $S$ factorizing completely through a commutati…

Support of Borelian Measures in Separable Banach Spaces

We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable belongs to some exponential Orlicz space, then the new subspace can be choose such that the norm of this variable in the new space also belongs to other exponential Orlicz space.

Riesz multiplier convergent spaces of operator valued series and a version of Orlicz- Pettis theorem

It is not usual to characterize an operator valued series via completeness of multiplier spaces. In this study, by using a series of bounded linear operators, we introduce the space $M^\infty_{R}\big(\sum_k T_k\big)$ of Riesz summability which is a generalization of the Cesàro summability. Therefore, we give the completeness criteria of these spaces with $c_0(X)$-multiplier convergent operator series. It is a natural consequence that one can characterize the completeness of a normed space through $M^\infty_{R}\big(\sum_k T_k\big)$ which will be assumed that is complete for every $c_0(X)$-multi…

Lack of compactness in the 2D critical Sobolev embedding, the general case

This paper is devoted to the description of the lack of compactness of the Sobolev embedding of $H^1(\R^2)$ in the critical Orlicz space ${\cL}(\R^2)$. It turns out that up to cores our result is expressed in terms of the concentration-type examples derived by J. Moser in \cite{M} as in the radial setting investigated in \cite{BMM}. However, the analysis we used in this work is strikingly different from the one conducted in the radial case which is based on an $L^ \infty$ estimate far away from the origin and which is no longer valid in the general framework. Within the general framework of $H…

Uniform convexity, reflexivity, supereflexivity and $B$ convexity of generalized Sobolev spaces $W^{1,Φ}$

We investigate Sobolev spaces $W^{1,Φ}$ associated to Musielak-Orlicz spaces $L^Φ$. We first present conditions for the boundedness of the Voltera operator in $L^Φ$. Employing this, we provide necessary and sufficient conditions for $W^{1,Φ}$ to contain isomorphic subspaces to $\ell^\infty$ or $\ell^1$. Further we give necessary and sufficient conditions in terms of the function $Φ$ or its complementary function $Φ^*$ for reflexivity, uniform convexity, $B$-convexity and superreflexivity of $W^{1,Φ}$. As corollaries we obtain the corresponding results for Orlicz-Sobolev spaces $W^{1,φ}$ where …

Combinatorial Inequalities and Subspaces of L1

Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2.

On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We present precise connections between M and f and establish conditions under which the distribution of a random variable f whose independent copies span l_M in L_p is essentially unique.

Nonlinear subsets of function spaces and spaceability

In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the same problem is studied for Nakano spaces assuming different hypothesis.

多线性交换子在Morrey空间中由VMO函数和分数积分算子生成的紧致性

Compactness of multilinear commutators generated by VMO functions and fractional integral operator on Morrey spaces

本文研究了由VMO函数和分数积分算子在Morrey空间中生成的多线性交换子的紧致性问题，通过分解tilde闭子空间来提升其紧致性。

On compact subsets of Sobolev spaces on manifolds

It is common that a Sobolev space defined on $\mathbb{R}^m$ has a non-compact embedding into an $L^p$-space, but it has subspaces for which this embedding becomes compact. There are three well known cases of such subspaces, the Rellich compactness, for a subspace of functions on a bounded domain (or an unbounded domain, sufficiently thin at infinity), the Strauss compactness, for a subspace of radially symmetric functions in $\mathbb{R}^m$, and the weighted Sobolev spaces. Known generalizations of Strauss compactness include subspaces of functions with block-radial symmetry, subspaces of funct…

Applications of the quantification of super weak compactness

We introduce a measure of super weak noncompactness $Γ$ defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the Banach spaces which are subspaces of a Hilbert generated space. The use of super weak compactness and $Γ$ casts light on the structure of these Banach spaces and complements the work of Argyros, Fabian, Farmaki, Godefroy, Hájek, Montesinos,\linebreak Troyanski and Zizler on this subject. A particular kind of relatively super weakly compact sets, namely uniformly weakly null sets, plays an important role and exhibits c…

Kolmogorov-Riesz紧性在渐近$L_p$空间中的扩展

Kolmogorov$\unicode{x2013}$Riesz compactness in asymptotic $L_p$ spaces

本文将经典的Kolmogorov-Riesz紧性定理扩展到渐近$L_p$空间中，引入了额外的几乎等界条件，以刻画相对紧性。

Multiplication operators on non-commutative spaces

Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting of quantum symmetric spaces. For non-endomorphic multiplication operators these properties can be completely characterized in the setting of quantum $L^p$-spaces and a partial solution obtained in the more general setting of quantum Orlicz spaces.