算子值矩阵的巴拿赫代数的维纳对

Lukas Köhldorfer, Peter Balazs
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引用次数: 0

摘要

在这篇文章中,我们介绍了维纳对的几个新例子$\mathcal{A}\subseteq \mathcal{B}$。\其中 $\mathcal{B} =\mathcal{B}(\ell^2(X;\mathcal{H}))$ 是作用于希尔伯特空间值的 Bochner 序列空间 $\ell^2(X.) 的有界算子的巴纳赫代数;(\mathcal{H})$和 $\mathcal{A} = \mathcal{A}(X)$是由某个相对分离的集合$X \subset \mathbb{R}^d$索引的算子值矩阵组成的巴拿赫代数。特别是,我们引入了$\mathcal{B}(\mathcal{H})$值版本的贾法尔代数、某些加权舒尔型代数、巴拿赫代数,它们是由比多项式衰减更一般的非对角线衰减条件定义的、Baskakov-Gohberg-Sj\"ostrand 代数的加权版本,以及所有这些矩阵代数的各向异性变化,并证明它们在 $\mathcal{B}(\ell^2(X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X., X;\(X;ell^2))$中反封闭。此外,我们还得到这些巴拿赫数组中的每一个都是对称的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Wiener pairs of Banach algebras of operator-valued matrices
In this article we introduce several new examples of Wiener pairs $\mathcal{A} \subseteq \mathcal{B}$, where $\mathcal{B} = \mathcal{B}(\ell^2(X;\mathcal{H}))$ is the Banach algebra of bounded operators acting on the Hilbert space-valued Bochner sequence space $\ell^2(X;\mathcal{H})$ and $\mathcal{A} = \mathcal{A}(X)$ is a Banach algebra consisting of operator-valued matrices indexed by some relatively separated set $X \subset \mathbb{R}^d$. In particular, we introduce $\mathcal{B}(\mathcal{H})$-valued versions of the Jaffard algebra, of certain weighted Schur-type algebras, of Banach algebras which are defined by more general off-diagonal decay conditions than polynomial decay, of weighted versions of the Baskakov-Gohberg-Sj\"ostrand algebra, and of anisotropic variations of all of these matrix algebras, and show that they are inverse-closed in $\mathcal{B}(\ell^2(X;\mathcal{H}))$. In addition, we obtain that each of these Banach algebras is symmetric.
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