Two properties of Müntz spaces

On Some Geometric Properties Of Sequence Space Defined By de la Vallee-Poussin Mean

In this work, we investigate k-nearly uniform convex(k-NUC) and the uniform Opial properties of the sequence space defined by de la Vallee-Poussin mean. Also we give some corollaries concerning the geometrical properties of this space.

Lipschitz-free spaces and Schur properties

In this paper we study $\ell_1$-like properties for some Lipschitz-free spaces. The main result states that, under some natural conditions, the Lipschitz-free space over a proper metric space linearly embeds into an $\ell_1$-sum of finite dimensional subspaces of itself. We also give a sufficient condition for a Lipschitz-free space to have the Schur property, the $1$-Schur property and the $1$-strong Schur property respectively. We finish by studying those properties on a new family of examples, namely the Lipschitz-free spaces over metric spaces originating from $p$-Banach spaces, for $p$ in…

On some properties of new paranormed sequence space of non-absolute type

In this work, we introduce some new generalized sequence space related to the space l(p). Furthermore we investigate some topological properties as the completeness, the isomorphism and also we give some inclusion relations between this sequence space and some of the other sequence spaces. In addition, we compute alpha-, beta- and gamma-duals of this space, and characterize certain matrix transformations on this sequence space.

On properties of multiplication and composition operators between Orlicz spaces

In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.

Structural properties of weak cotype 2 spaces

Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed proportional dimension are proved.

Free Banach spaces and the approximation properties

We characterize the metric spaces whose free space has the bounded approximation property through a Lipschitz analogue of the local reflexivity principle. We show that there exist compact metric spaces whose free spaces fail the approximation property.

Approximation properties and Schauder decompositions in Lipschitz-free spaces

We prove that the Lipschitz-free space over a doubling metric space has the bounded approximation property. We also show that the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone finite-dimensional Schauder decompositions.

控制混合光滑空间中傅里叶变换的映射性质

Mapping properties of the Fourier transform in spaces with dominating mixed smoothness

该论文聚焦控制混合光滑函数空间，探究傅里叶变换的连续及紧映射特性，为相关函数空间理论提供映射性质层面的研究支撑。

Köthe-Bochner spaces and some geometric properties related to rotundity and smoothness

In 2000 Kadets et al. introduced the notions of acs, luacs and uacs spaces, which form common generalisations of well-known rotundity and smoothness properties of Banach spaces. In a recent preprint the author introduced some further related notions and investigated the behaviour of these geometric properties under the formation of absolute sums. This paper is in a sense a continuation of the previous work. Here we will study the behaviour of said properties under the formation of Köthe-Bochner spaces, thereby generalising some results of Sirotkin on the acs, luacs and uacs properties of $L^p$…

Some Geometric and Topological Properties of a New Sequence Space Defined by De la Vallee-Poussin Mean

The main purpose of this paper is to introduce a new sequence space by using de la Vallee-Poussin mean and investigate both the modular structure with some geometric properties and some topological properties with respect to the Luxemburg norm.

On the properties of Ascent and Descent of Composition operator on Orlicz spaces

Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.

New properties of grand amalgam spaces

In $ \left[14\right]$, a new family called grand amalgam space $W( L^{p),θ},L^{q),θ})$ of amalgam spaces was defined and investigated properties of these spaces. The present paper is a sequel to my work $[14].$ In this paper, notations are included in Section 1. In Section 2, we introduce another equivalent but discrete definition of grand amalgam space and study properties of these spaces. In Section 3, we determine necessary and sufficient conditions on a locally compact Abelian group $G$ for the grand amalgam spaces $W(L^{p,)θ},L^ {q,θ})$ to be an algebra under convolution.

Properties of parabolic Sobolev and parabolic Besov spaces

In this paper, we characterize parabolic Besov and parabolic Sobolev spaces in ${\bf R}^{n+1}$ and ${\bf R}^{n+1}_T, \,\, T > 0$. We also, study the relation between parabolic Besov spaces in ${\bf R}^{n}_T, \,\, T > 0$ and standard Besov space in $\R$.

On Some Properties of Measurable Functions in Abstract Spaces

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

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.

Some convexity properties in direct integrals and Köthe-Bochner spaces

The notion of direct integrals introduced by Haydon, Levy and Raynaud in 1991 is a generalisation of the well-known concept of Köthe-Bochner spaces of vector-valued functions (using a family of target spaces instead of just one space). Here we will discuss some classical geometric properties like strict convexity, local uniform convexity and uniform convexity in direct integrals. We will also consider strongly convex and very convex Köthe-Bochner spaces.

Schatten properties of Toeplitz operators on the Paley-Wiener space

We collect several old and new descriptions of Schatten class Toeplitz operators on the Paley-Wiener space and answer a question on discrete Hilbert transform commutators posed by Richard Rochberg.

On certain geometric properties in Banach spaces of vector-valued functions

We consider a certain type of geometric properties of Banach spaces, which includes for instance octahedrality, almost squareness, lushness and the Daugavet property. For this type of properties, we obtain a general reduction theorem, which, roughly speaking, states the following: if the property in question is stable under certain finite absolute sums (for example finite $\ell^p$-sums), then it is also stable under the formation of corresponding Köthe-Bochner spaces (for example $L^p$-Bochner spaces). From this general theorem, we obtain as corollaries a number of new results as well as some …

Properties of Kondratiev spaces

In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compact embeddings, and in addition we shall deal with pointwise multiplication in these spaces.

Certain properties of Generalization of $L^p-$Spaces for $0 < p < 1$

This paper introduces the notion of $N^*-$function and gives a generalization of $L^p,$ for $0<p<1$ denoted by $L_Φ$ where $Φ$ is an $N^*-$function. As well as, this paper examines some properties regarding to this generalized spaces and its linear forms, including some analogies and common features to some other well known spaces. As well as, we prove this space is a quasi-normed space but it is not normed space.

A note on the some geometric properties of the sequence spaces defined by Taylor method

In this paper, it was obtained the new matrix domain with the well known classical sequence spaces and an infinite matrix. The Taylor method which known then as the circle method of order r (0 < r < 1), as an infinite matrix for the matrix domain is used. Newly constructed space is isomorphic copy of the spaces of all absolutely p-summable sequences. It is well known that Hilbert space have the nicest geometric properties. Then, it is proved that the new space is a Hilbert space for p = 2. Further, it was computed dual spaces and characterized some matrix classes of the new Taylor space in the…

计算巴拿赫空间中某些几何性质的博雷尔复杂度

Computing Borel complexity of some geometrical properties in Banach spaces

该研究计算了巴拿赫空间中直径二性质、道加瓦特定理空间等几何性质类别的博雷尔复杂度，多数情况达最优，完善了近年巴拿赫空间同构类相关研究。

On Geometric properties of Henstock-Orlicz spaces

In this paper we extend the theory of Henstock-Orlicz spaces with respect to vector measure. We study the integral representation of operators. Lastly we study Uniformly convexity, reflexivity and the Radon-Nikodym property of the Henstock-Orlicz spaces

Continuity properties of sequentially asymptotically center-complete spaces

We obtain formulae to calculate the asymptotic center and radius of bounded sequences in ${\cal C}_0(L)$ spaces. We also study the existence of continuous selectors for the asymptotic center map in general Banach spaces. In Hilbert spaces, even a Hölder-type estimation is given.

Classification of Banach Spaces --its Topological and Cardinality Properties

Classes of Banach spaces that are finitely, strongly finitely or elementary equivalent are introduced. On sets of these classes topologies are defined in such a way that sets of defined classes become compact totally disconnected topological spaces. Results are used in the problem of synthesis of Banach spaces, and to describe omittable spaces that are defined below.

分数阶 Musielak-Sobolev 空间的密度性质

Density properties for fractional Musielak-Sobolev spaces

本文定义了一个新的分数阶 Musielak-Sobolev 空间，并证明了其中光滑紧支撑函数的密度性质。

Absolute sums of Banach spaces and some geometric properties related to rotundity and smoothness

We study the notions of acs, luacs and uacs Banach spaces which were introduced by V. Kadets et al. in 2000 and form common generalisations of the usual rotundity and smoothness properties of Banach spaces. In particular, we are interested in (mainly infinite) absolute sums of such spaces. We also introduce some new classes of spaces that lie inbetween those of acs and uacs spaces and study their behaviour under the formation of absolute sums as well.

Non-squareness and local uniform non-squareness properties of Orlicz-Lorentz function spaces endowed with the Orlicz norm

In this paper the necessary and sufficient conditions were given for Orlicz-Lorentz function space endowed with the Orlicz norm having non-squareness and local uniform non-squareness.

Linear properties of Banach spaces and low distortion embeddings of metric graphs

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to a subspace of a Banach space $X$.

Some properties of K-frame in n-Hilbert space

The notion of a K-frame in n-Hilbert space is presented and some of their characterizations are given. We verify that sum of two K-frames is also a K-frame in n-Hilbert space. Also, the concept of tight K-frame in n-Hilbert space is described and some properties of its are going to be established.

Operators in Rigged Hilbert spaces: some spectral properties

A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.

Diameter two properties in James spaces

We study the diameter two properties in the spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the topological dual space of the previous Banach spaces fails every diameter two property. However, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norm of these spaces is octahedral. Also we find a closed hyperplane $M$ of $JH_\infty$ whose topological dual space enjoys the $w^*$-strong diameter two property and also $M$ and $M^*$ have an octahedral norm.

赫茨型索伯列夫空间中的乘法性质与雷利奇 - 康德拉乔夫定理

Multiplication properties and the Rellich-Kondrachov theorem in Herz-type Sobolev spaces

证明赫茨型索伯列夫空间构成巴拿赫代数并建立其雷利奇 - 康德拉乔夫紧致性定理，扩展经典理论，表明该空间是经典索伯列夫空间的自然推广。

论 Banach 空间中直径二性质与理想之间的对偶性

On the duality between Diameter Two Properties and Ideals in Banach Spaces

本文研究 Banach 空间中直径二性质与 M-理想的对偶关系，证明 M-理想的对偶继承各类 $w^*$ 直径二性质，并以反例说明逆命题不成立，进而考察 $C(K)$ 空间及其对偶。

某些积分算子的映射性质

Mapping properties of certain integral operators

本文研究具有特殊核的二维线性积分算子在加权Sobolev--Slobodetskii型空间及其Banach推广中的映射性质，给出了有界性的充分条件。

Some Properties of Accretive Operators in Linear 2-Normed Spaces

In this paper we discuss some properties of resolvents of an accretive operator in linear 2-normed spaces, focusing on the concept of contraction mapping and the unique fixed point of contraction mappings in linear 2- normed spaces. Also, we establish the existence of solution of strong accretive operator equation in linear 2-normed spaces.

${\mathcal F}$-Hypercyclic and disjoint ${\mathcal F}$-hypercyclic properties of binary relations over topological spaces

In this paper, we examine various types of ${\mathcal F}$-hypercyclic (${\mathcal F}$-topologically transitive) and disjoint ${\mathcal F}$-hypercyclic (disjoint ${\mathcal F}$-topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.

New Proofs on Properties of an Orthogonal Decomposition of a Hilbert Space

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions, particularly between those which are non zero constant multiples of each other and between functions from the kernel space and the derivative image of the trace less Sobolev space.

Domination properties and extension of positive compact operators on pre-Riesz spaces

This paper concerns positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space to the Riesz completion. It extends the order continuous norms in pre-Riesz spaces to Riesz completions. The compactness of third power of a positive operator is obtained in a pre-Riesz space which has an order unit.

Inclusion properties of Orlicz and weak Orlicz spaces

In this paper we discuss the structure of Orlicz spaces and weak Orlicz spaces on $\mathbb{R}^n$. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the characteristic functions of the balls in $\mathbb{R}^n$.

关于在Lipschitz-free空间中实现直径二性质的注记

A note on attaining diameter two properties in Lipschitz-free spaces

本文证明在Lipschitz-free空间中，强直径二性质、直径二性质和局部直径二性质与其对应的实现变体一致。

On Properties of Symmetric Banach Function spaces and Peetre's Interpolation Spaces

A set of all symmetric Banach function spaces defined on [0,1] is equipped with the partial order by the relation of continuous inclusion. Properties of symmetric spaces, which do not depend of their position in the ordered structure, are studied. With the help of the J. Peetre's interpolation scheme it is shown that for any pair of symmetric spaces E, F such that F is absolutely continuously included in E there exists an intermediate (so called, Peetre's) space K(E,F;W), where W is a space with an unconditional basis, that is reflexive or, respectively, weakly sequentially complete provided W…

Lebesgue空间中多元分形函数的一些分析性质

Some Analytical Properties of Multivariate Fractal Functions in Lebesgue Spaces

本文构造了Lebesgue空间中的多元分形函数，分析了相关分形算子的性质，并证明了空间$\mathcal{L}^q(I^n, μ_p)$中相关分形函数存在Schauder基。

关于单位ary duals of compact groups上$\ell^{p}$-空间的几何性质

On geometric properties of $\ell^{p}$-spaces on unitary duals of compact groups

本文研究了紧致群的单位ary dual上$\ell^{p}$-空间的几何性质，证明了其均匀光滑性、均匀凸性、Clarkson不等式等，并探讨了类型和余类型性质。

On some properties of relative capacity and thinness in weighted variable exponent Sobolev spaces

In this paper, we define weighted relative $p(.)$-capacity and discuss properties of capacity in the space $W_{\vartheta }^{1,p(.)}(\mathbb{R}^{n}).$ Also, we investigate some properties of weighted variable Sobolev capacity. It is shown that there is a relation between these two capacities. Moreover, we introduce a thinness in sense to this new defined relative capacity and prove an equivalence statement for this thinness.

Dynamics of composition operators on function spaces defined by local and global properties

In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong operator topology.

Compositions of projections in Banach spaces and relations between approximation properties

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $π$-property in terms of norms of compositions of projections is found.

Commutativity and spectral properties of $k^{th}$-order slant little Hankel operators on the Bergman space

In this paper, we introduce the notion of $k^{th}$-order slant little Hankel operator on the Bergman space with essentially bounded harmonic symbols on the unit disc and obtain its algebraic and spectral properties. We have also discussed the conditions under which $k^{th}$-order slant little Hankel operators commute.

On Inclusion Properties of Two Versions of Orlicz-Morrey Spaces

There are two versions of Orlicz-Morrey spaces (on $\mathbb{R}^n$), defined by Nakai in 2004 and by Sawano, Sugano, and Tanaka in 2012. In this paper we discuss the inclusion properties of these two spaces and compare the results. Computing the norms of the characteristic functions of balls in $\mathbb{R}^n$ is one of the keys to our results. Similar results for weak Orlicz-Morrey spaces of both versions are also obtained.

关于序列空间的若干精细性质

On Certian Fine Properties of Sequence Spaces

本文发展Orlicz与Lorentz--Zygmund序列空间理论，刻画其满足重排不变Banach序列空间公理的参数、基本函数渐近行为及关联空间，并完全刻画两类空间重合的条件。

On algebraic properties of sets of Banach ideal function spaces

It is shown that every set I(m) of Banach lattices of measurable functions defined on a measure space (Q,S,m), equipped with a some natural ordering became a modular lattice, which is Dedekind complete provided m is a probability measure. Moreover, some natural operations on considered spaces are in Galois connexion.

关于光滑巴拿赫空间上正规算子和自伴随算子的性质

On properties of normal operators and self-adjoint operators on smooth Banach spaces

本文探讨光滑巴拿赫空间上正规和幺正算子的性质，扩展了从希尔伯特空间到巴拿赫空间的经典概念，并研究自伴随算子的范数、最小模、数值半径等性质及谱特性。

Global properties of Dirichlet forms on discrete spaces

We provide an introduction to Dirichlet forms on discrete spaces and study their global properties such as recurrence, stochastic completeness and regularity of the Neumann form. In this setting we compare the notion of a recurrent Dirichlet form and a recurrent discrete time Markov chain of a given graph. We prove several known and several new characterizations of recurrence by using functional analytic Dirichlet form methods only. Finally, we compare all the mentioned global properties and discuss their relation to spectral theory.

Inclusion Properties of Weighted Weak Orlicz Spaces

In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces. Next, we also obtain similar results on weighted weak Orlicz spaces. One of the keys to prove our results is to use the norm of the characteristic functions of the balls in $\mathbb{R}^n$.