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Wiener pairs of Banach algebras of operator-valued matrices
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Mathematics - Functional Analysis
Mathematics - Operator Algebras
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.16416
- Document Type :
- Working Paper