Ali Ebadian, Saeed Hashemi Sababe, Maysam Zallaghi
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular we tried to extend this concept and prove some theorems.
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This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.
We prove the boundedness of a general class of multipliers and Fourier multipliers, in particular of the Hilbert transform, on quasi-Banach modulation spaces. We also deduce boundedness for multiplications and convolutions for elements in such spaces.
We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it results necessary that such sequence must be a $X_d$-Riesz basis and a sampling basis for the space. These results are a generalization of some already known sampling theorems over reproducing kernel Hilbert spaces.
In this paper, we introduce (p,q)g-Bessel multipliers in Banach spaces and we show that under some conditions a (p,q)g-Bessel multiplier is invertible. Also, we show the continuous dependency of (p,q)g-Bessel multipliers on their parameters.
Sampling in reproducing kernel Banach spaces on Lie groups
给出了李群上再生核巴拿赫空间的采样定理。最近的方法来解决这个问题依赖于可积的内核和它的本地振荡。在本文中，我们取代可积性条件的再生核的导数的要求。然后，使用的结果来获得框架和原子分解的巴拿赫空间的分布源于循环表示，它表明，这是特别容易的，当循环向量是一个Gårding向量的平方可积〔的〕表示。
Multipliers and Toeplitz operators on Banach spaces of sequences
证明了Z上的一大类序列的巴拿赫空间上的每个乘子M（与移位算子交换的有界算子）都对应于一个在S的谱上以M的范数本质有界的函数.
The dynamic behavior of conjugate multipliers on some reflexive Banach spaces of analytic functions
本文在自反解析函数空间中推广Godefroy和Shapiro的工作，完整刻画了共轭乘子的超循环性、混合性与混沌性。
We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford-Pettis criterion) coincides with the class of 1-disjointly homogeneous Banach lattices. A new examples of such spaces are provided. Furthermore, it is shown that Dunford-Pettis criterion is equivalent to de la Vallee Poussin criterion in all rearrangement invariant spaces on the interval. Finally, the results are applied to characterize weakly compact pointwise multipliers between Banach function lattices.
For 1 ≤ p < ∞, it is known that the set K^*_p contains of all Lambert multipliers acting between L^p-spaces is a Banach space. In this study, we introduce a new induced norm by conditional expectation operators to show that K^*_p is a commutative Banach algebra with respect to this norm. Furthermore, in main result, the Fredholm *-multiplication operators on L^p-spaces are characterized, and some more results are obtained.
Vector-valued Reproducing Kernel Banach Spaces with Group Lasso Norms
该研究为稀疏多任务学习的核方法建立数学基础，构建了带$\ell_{p,1}$群Lasso范数的向量值再生核巴拿赫空间，证明其满足线性表示定理并提出适配的再生核，可用于稀疏多任务学习。
Generalized Reproducing Kernel Banach Spaces: A Functional Analytic Framework for Abstract Neural Networks
本文提出广义再生核巴拿赫空间框架，用于构建抽象神经网络，扩展了传统RKBS在处理巴拿赫值余域问题中的应用，推动了神经架构设计与数学建模的结合。
Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. We introduce and study the notions of $n$-multipliers and approximate local $n$-multipliers by generalizing the classical concept of multipliers from $A$ into $X$. As an algebraic result, we construct a Banach algebra consisting of $n$-multipliers on $A$ and under some mild conditions, we give a nice relation of this algebra with $n$-homomorphisms from $A$ into $\mathbb{C}$.
In this paper we introduce the concept of von Neumann-Schatten Bessel multipliers and obtain some of their characterizations. Finally, special attention is devoted to the study of invertible Hilbert--Schmidt frame multipliers. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for diagonalization of matrices in finite dimensional setting as well as for dual $g$-frames. In particular, we show that a $g$-frame is uniquely determined by the set of its $g$-frames.
Let ${\mathcal A}$ be a Banach algebra and let $φ$ be a non-zero character on ${\mathcal A}$. Suppose that ${\mathcal A}_M$ is the closure of the faithful Banach algebra ${\mathcal A}$ in the multiplier norm. In this paper, topologically left invariant $φ$-means on ${\mathcal A}_M^*$ are defined and studied. Under some conditions on ${\mathcal A}$, we will show that the set of topologically left invariant $φ$-means on ${\mathcal A}^*$ and on ${\mathcal A}_M^*$ have the same cardinality. We also study the left uniformly continuous functionals associated with these algebras. The main application…
Targeting at sparse multi-task learning, we consider regularization models with an $\ell^1$ penalty on the coefficients of kernel functions. In order to provide a kernel method for this model, we construct a class of vector-valued reproducing kernel Banach spaces with the $\ell^1$ norm. The notion of multi-task admissible kernels is proposed so that the constructed spaces could have desirable properties including the crucial linear representer theorem. Such kernels are related to bounded Lebesgue constants of a kernel interpolation question. We study the Lebesgue constant of multi-task kernels…
In this paper, we characterize the (left) multiplier algebra of a semidirect product algebra ${\mathcal A}={\mathcal B}\oplus {\mathcal I}$, where ${\mathcal I}$ and ${\mathcal B}$ are closed two-sided ideal and closed subalgebra of ${\mathcal A}$, respectively. As an application of this result we investigate the BSE-property of this class of Banach algebras. We then for two commutative semisimple Banach algebras ${\mathcal A}$ and ${\mathcal B}$ characterize the BSE-functions on the carrier space of ${\mathcal A}\times_ϕ{\mathcal B}$, the $ϕ$-Lau product of ${\mathcal A}$ and ${\mathcal B}$, …
The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calderón's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing kernels.
This article develops optimality conditions for a large class of non-smooth variational models. The main results are based on standard tools of functional analysis and calculus of variations. Firstly we address a model with equality constraints and, in a second step, a more general model with equality and inequality constraints, always in a general Banach space context. We highlight the results in general are well known, however, some novelties are introduced related to the proof procedures, which are in general softer than those concerning the present literature.
Vector-valued Reproducing Kernel Banach Spaces with Applications to Multi-task Learning
受巴拿赫空间多任务机器学习的启发，我们提出了向量值再生核巴拿赫空间（RKBS）的概念。研究了空间的基本性质和相应的再生核。我们还提出了特征图的建设和向量值RKBS的几个具体的例子。然后将该理论应用于多任务机器学习。特别地，建立了向量值RKBS中正则化学习方案的极小元的表示定理和特征方程。
We prove various extensions of the Coifman-Rubio de Francia-Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call $\ell^{r}(\ell^{s})$-boundedness, which implies $\mathcal{R}$-boundedness in many cases. The proofs are based on new Littlewood-Paley-Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.
Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach
本文利用再生核 Banach 空间框架和半内积，为 Hardy 和 Bergman 空间等函数空间中的插值问题提供了寻找最小范数解的系统方法，并给出数值示例。
Multipliers on a new class of Banach algebras, locally compact quantum groups, and topological centres
本文研究了一大类巴拿赫代数的乘子代数，这类代数包括局部紧群$G$的群代数$L_1(G)$，Beurling代数$L_1(G, ω)$和Fourier代数$A(G)$.本文通过抽象的Banach代数方法得到了许多新的结果，并统一了关于$L_1(G)$和$A(G)$的一些已有定理.在局部紧量子群上的乘子的表示和拓扑中心问题上得到了应用。特别是解决了抽象调和分析中的五个公开问题。
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First we verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, we develop a new concept of generalized …
Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces
本文证明Fourier乘子从L^Φ1到L^Φ2的连续性可推广至Orlicz调制空间，并应用于Mihlin和Hörmander定理，最后给出特定符号乘子在拟Banach Orlicz调制空间上的有界性条件。
Multipliers for p-Bessel sequences in Banach spaces
乘子最近被引入作为希尔伯特空间中贝塞尔序列和框架的算子。这些运算符由插入在分析和合成运算符之间的固定乘法模式（符号）定义。本文推广了巴拿赫空间中p-Bessel和p-Riesz序列的Bessel乘子的概念。它将表明，有界符号导致有界算子。收敛到零的符号诱导出紧算子。此外，我们还给出了乘子是核型算子的充分条件。最后，我们将展示乘数对其参数的连续依赖性。
Quasi-multipliers of Hilbert and Banach C*-bimodules
Hilbert C*-双模V的拟乘子是由Brown，Mingo和Shen在1994年引入的，作为Banach双对偶模V** 的一个子集。我们使用中心化子的方法给出了Hilbert C*-双模的拟乘子的另一个（等价）定义，然后证明了拟乘子实际上是某个范畴的泛（极大）对象。我们还引入了Kasparov意义下的双模的拟乘子，甚至引入了C* 代数上的Banach双模的拟乘子，只要这些C* 代数是非退化的.利用拟严格拓扑给出了拟乘子的拓扑图。最后，我们描述了两种主要情况下的拟乘子：标准Hilbert双模l_2（A）和局部紧空间上Hilbert C*-双模丛的截面的双模。
Multipliers, Self-Induced and Dual Banach Algebras
在论文的第一部分中，我们对巴拿赫代数和完全压缩的巴拿赫代数的乘子或双中心化子理论进行了简短的综述。我们的方法是非常代数的：这是一个故意试图分离本质上代数参数从拓扑参数。我们集中在如何扩展模块的行动，和同态，从代数乘子代数的问题。然后，我们考虑的特殊情况下，我们有一个有界的近似身份，当我们的代数是自诱导。第二部分主要研究对偶巴拿赫代数。我们给出了一个简单的判定乘子代数是对偶巴拿赫代数的准则。应用这一点证明了局部紧量子群的卷积代数的乘子代数总是对偶巴拿赫代数。我们还研究了这个问题的抽象庞特里亚金对偶的框架内，并表明，我们构造相同的弱$^*$ -拓扑。我们探讨了一个Hopf卷积代数的概念，并表明，在许多情况下，使用扩展的Haagerup张量积可以取代乘子代数。
In this paper we introduce the notion of weak differential subordination for martingales and show that a Banach space $X$ is a UMD Banach space if and only if for all $p\in (1,\infty)$ and all purely discontinuous $X$-valued martingales $M$ and $N$ such that $N$ is weakly differentially subordinated to $M$, one has the estimate $\mathbb E \|N_{\infty}\|^p \leq C_p\mathbb E \|M_{\infty}\|^p$. As a corollary we derive the sharp estimate for the norms of a broad class of even Fourier multipliers, which includes e.g. the second order Riesz transforms.
Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In particular, we prove a representer theorem for a wide class of reproducing kernel Banach spaces that admit a suitable integral representation and include one hidden layer neural networks of possibly infinite width. Further, we show that, for a suitable class of ReLU activation functions, the norm in the corresponding reproducing kernel Banach space can be charact…
We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.
We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the symmetrization commutes with these operations. We determine also the spaces of pointwise multipliers between Lorentz spaces and Cesaro spaces. Developed methods may be regarded as an arithmetic of quasi-Banach function spaces and proofs of Theorems 3, 4 and 6 give a kind of tutorial for these methods. Finally, the above results will be used in proofs of some facto…
Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces
研究高斯过程与再生核巴拿赫空间中高斯随机元之间的联系，通过γ-拉德尼化算子刻画协方差算子对应的正定函数，并将经典Driscoll定理推广到巴拿赫空间。
The notion of multipliers in Hilbert space was introduced by Schatten in 1960 using orthonormal sequences and was generalized by Balazs in 2007 using Bessel sequences. This was extended to Banach spaces by Rahimi and Balazs in 2010 using p-Bessel sequences. In this paper, we further extend this by considering Lipschitz functions. On the way we define frames for metric spaces which extends the notion of frames and Bessel sequences for Banach spaces. We show that when the symbol sequence converges to zero, the multiplier is a Lipschitz compact operator. We study how the variation of parameters i…
Decomposition of one-layer neural networks via the infinite sum of reproducing kernel Banach spaces
本文利用RKBS特征定理定义RKBS的和并证明其与特征空间直和相容，将积分RKBS分解为p-范数RKBS之和，为单层神经网络及积分RKBS类的结构理解提供应用。
Reproducing Kernel Banach Spaces with the l1 Norm II: Error Analysis for Regularized Least Square Regression
估计正则化学习方案的学习率的典型方法是通过采样误差、假设误差和正则化误差之和来限制近似误差。使用满足线性表示定理的再生核空间带来了自动从和中丢弃假设误差的优点。按照这个方向，我们说明了如何再生核Banach空间与l1范数可以应用于提高学习率估计的l1正则化在机器学习。
Reproducing Kernel Hilbert spaces (RKHS) have been a very successful tool in various areas of machine learning. Recently, Barron spaces have been used to prove bounds on the generalisation error for neural networks. Unfortunately, Barron spaces cannot be understood in terms of RKHS due to the strong nonlinear coupling of the weights. This can be solved by using the more general Reproducing Kernel Banach spaces (RKBS). We show that these Barron spaces belong to a class of integral RKBS. This class can also be understood as an infinite union of RKHS spaces. Furthermore, we show that the dual spa…
We give a modified definition of a reproducing kernel Hilbert $C^*$-module (shortly, $RKHC^*M$) without using the condition of self-duality and discuss some related aspects; in particular, an interpolation theorem is presented. We investigate the exterior tensor product of $RKHC^*M$s and find their reproducing kernel. In addition, we deal with left multipliers of $RKHC^*M$s. Under some mild conditions, it is shown that one can make a new $RKHC^*M$ via a left multiplier. Moreover, we introduce the Berezin transform of an operator in the context of $RKHC^*M$s and construct a unital subalgebra of…
Featured Reproducing Kernel Banach Spaces for Learning and Neural Networks
本文提出了一种基于特色再生核巴拿赫空间的框架，用于在巴拿赫空间中进行学习，扩展了核方法和神经网络的应用范围。
Compact multipliers on spaces of analytic functions
本文研究单位圆盘上的解析函数的巴拿赫空间上的紧乘子算子，其值域在Banach序列格上。若定义域空间$X$满足$H_\infty\hookrightarrow X\hookrightarrow H_1$，则给出了紧性的充要条件.在定义域空间$X$满足$H_\infty\hookrightarrow X\hookrightarrow H_2$的情况下，利用Banach序列格上对角算子非紧性的Hausdorff测度的计算，得到了紧乘子的特征.
In this paper we give an example of a Banach algebra $A$ and a closed ideal $I$ of $A$ such that the multiplier algebra of $I$ is equal to $A$ but $I$ does not have any bounded approximate identity. In the case that $I$ has an approximate identity, we give a necessary condition on $I$ for which $A=\mathcal{M}(I)$, where $\mathcal{M}(I)$ denotes the multiplier algebra of $I$. Finally, as a corollary of our results, we show that the Fourier algebra of an amenable group is strictly dense in the Fourier-Stieltjes algebra.
Deformations of Reproducing Kernel Hilbert Spaces on Homogeneous Subvarieties of the Unit Ball
研究单位球齐次子流形、其再生核希尔伯特空间及乘子代数关系，证明RKHS等距同构时乘子代数也同构，对于易处理齐次流形，乘子代数同构或有酉变换关系时，相关RKHS也等距同构。
Weighted function spaces: convolutors, multipliers, and mollifiers
本文研究Gelfand-Shilov型加权光滑函数空间，引入紧支集光滑函数对的矩向分解性质，通过磨光化方法完整刻画了该类空间及对应的卷积子、乘子空间，明确了相关算子与权函数系统的作用关系。
Infinite order decoupling of random chaoses in Banach space
证明了巴拿赫空间中系数非齐次随机多项式的若干解耦不等式。齐次分量的次数作为某些庞加莱型多项式项的乘子的指数进入比较。结果表明，大多数类型的解耦不等式的实现都依赖于巴拿赫空间的几何性质。
Reproducing Kernel Banach Spaces with the l1 Norm
针对稀疏学习问题，我们构造了输入空间X上的函数Banach空间B，其性质是：（1）B具有l1范数，即它关于计数测度与X上的可积函数Banach空间同构：（2）点评价是B上的连续线性泛函，并且可以用带核函数的双线性形式表示;（3）B上的正则化学习方案满足线性表示定理。核函数的例子，允许这样的空间的建设。
Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis. Existing constructions include the reflexive RKBS via a bilinear form, the semi-inner-product RKBS, the RKBS with $\ell^1$ norm, the $p$-norm RKBS via generalized Mercer kernels, etc. The definitions of RKBS and the associated reproducing kernel in those references are dependent on the construction. Moreover, relations among those constructions are unclear. We expl…
General Hormander and Mikhlin conditions for multipliers of Besov spaces
本文引入了巴拿赫空间几何的一个新的条件，得到了加权Besov空间中的算子值Fourier乘子定理。特别地，建立了巴拿赫空间几何与Hormander-Mikhlin条件之间的联系.作为主要结果的应用，研究了退化椭圆型微分算子方程的正则性。
Hyperbolicity of semigroups and Fourier multipliers
利用生成元的预解式的Fourier乘子性质给出了巴拿赫空间上强连续半群双曲性的一个刻画。还考虑了关于经典解的双曲性。我们的方法统一和简化了M。Kaashoek- S. Verduyn Lunel理论和S.克拉克，M。Hieber，S. Montgomery-Smith，F. Räbiger，T. Randolph和L.维斯
We show that the analyticity of semigroups $(T_t)_{t \geq 0}$ of (not necessarily positive) selfadjoint contractive Fourier multipliers on $\mathrm{L}^p$-spaces of any abelian locally compact group is preserved by the tensorisation of the identity operator $\mathrm{Id}_X$ of a Banach space $X$ for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. The result is even new for semigroups of Fourier multipliers acting on $\mathrm{L}^p(\mathbb{R}^n)$. The proof relies on the use of noncommutative Banach spaces and we give a more general result for semigroups of Fou…
Neural reproducing kernel Banach spaces and representer theorems for deep networks
本文证明深度神经网络可定义再生核Banach空间，其范数具有稀疏性以适应数据隐结构，并借助变分方法推导表示定理，为实际有限网络架构提供理论依据。
Which Spaces can be Embedded in $L_p$-type Reproducing Kernel Banach Space? A Characterization via Metric Entropy
本文建立了度量熵增长与函数空间嵌入再生核希尔伯特/巴拿赫空间能力之间的新联系，证明了度量熵有界可嵌入$L_p$型再生核巴拿赫空间，揭示了核方法在复杂函数空间学习中的能力与局限。
Let $H$ be an ultraspherical hypergroup associated to a locally compact group $ G $ and let $A(H)$ be the Fourier algebra of $H$. For a left Banach $A(H)$-submodule $X$ of $VN(H)$, define $Q_X$ to be the norm closure of the linear span of the set $\{uf: u\in A(H), f\in X\}$ in $B_{A(H)}(A(H), X^*)^*$. We will show that $B_{A(H)}(A(H), X^*)$ is a dual Banach space with predual $Q_X$, we characterize $Q_X$ in terms of elements in $A(H)$ and $ X$. Applications obtained on the multiplier algebra $ M(A(H))$ of the Fourier algebra $ A(H)$. In particular, we prove that $ G $ is amenable if and only i…
Unconditionality, Fourier multipliers and Schur multipliers
设$G$是无限局部紧交换群.若$X$是Banach空间，证明了若$L^2(G)$上的有界Fourier乘子$T$具有$T\ot Id_X$在$L^2(G,X)$上有界的性质，则Banach空间$X$同构于Hilbert空间.此外，如果$1<p<\infty$，$p\not=2$，我们证明了在$L^p(G)$上存在一个不完全有界的有界Fourier乘子.最后，我们从舒尔乘数的角度来考察无条件性。更确切地说，我们给出了几个充要条件，以确定是否一个算子空间是完全同构的算子Hilbert空间。
Ridgelet Transforms of Functions in Banach lattices
本文在Banach格框架下建立Ridgelet变换在R^n上的再生公式，基于k平面Radon变换和小波型重建算子，证明其在格范数和几乎处处收敛，并提出小波函数的可接受条件，获得函数在Banach格中的显式反演公式。
In this paper, we propose to define the concept of family of local atoms and then we generalize this concept to the atomic system for operator in Banach spaces by using semi-inner product. We also give a characterization of atomic systems leading to obtain new frames. In addition, a reconstruction formula is obtain. Next, some new results are established. The characterization of atomic systems allows us to state some results for sampling theory in semi-inner product reproducing kernel Banach spaces. Finally, having used frame operator in Banach spaces, new perturbation results are established.
In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are $\mathcal{R}$-boundedness results for Fourier multiplier operators, which are of independent interest. As an application we characterize the pointwise multiplier property of the indicator function of the half-space on these spaces. All results are proved in the setting of weighted spaces.
In this article we investigate some general properties of the multiplier algebras of normed spaces of continuous functions (NSCF). In particular, we prove that the multiplier algebra inherits some of the properties of the NSCF. We show that it is often possible to construct NSCF's which only admit constant multipliers. In order to do that, using a method from [23], we prove that any separable Banach space can be realized as a NSCF over any separable metrizable space. On the other hand, we give a sufficient condition for non-separability of a multiplier algebra.
Let $G$ be a locally compact group and $p,q\in \mathbb{R}$ with $p>1$ $p\not=2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2$, if $p>2$ then $2<q<p.$) The main result of the paper is that $A_q(G)$ multiplies $A_p(G)$, more precisely we show that the Banach algebra $A_p(G)$is a Banach module on $A_q(G).$
A Homomorphism Theorem for Bilinear Multipliers
本文证明了局部紧阿贝尔群（LCA）中双线性乘子的一个抽象同态定理。我们还提供了一些应用程序。特别地，我们得到了K的一个双线性抽象形式。强、弱型双线性乘子的de Leeuw定理我们还得到了非紧LCA群上双线性乘子的必要条件，得到了相应算子在重排不变空间乘积上的有界性。我们的研究将欧几里得空间中已有的一些结果推广到一般LCA群的框架下，并得到了拟巴拿赫空间中双线性乘子的有界性的新结果.
We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna-Pick (CNP) kernel. For such a densely defined operator $T$, the domains of $T$ and $T^*$ are reproducing kernel Hilbert spaces contractively contained in the ambient space. We study several aspects of these spaces, especially the domain of $T^*$, which can be viewed as analogs of the classical deBranges-Rovnyak spaces in the unit disk.
Essential norms of pointwise multipliers in the non-algebraic setting
本文计算了在不同Köthe空间之间作用的乘法算子的本质范数和弱本质范数，探讨了Banach序列空间和单位圆上解析函数空间的相关应用。
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