Wiener pairs of Banach algebras of operator-valued matrices
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916566072819712 |
|---|---|
| author | Köhldorfer, Lukas Balazs, Peter |
| author_facet | Köhldorfer, Lukas Balazs, Peter |
| contents | 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-Sjöstrand 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wiener pairs of Banach algebras of operator-valued matrices Köhldorfer, Lukas Balazs, Peter Functional Analysis Operator Algebras 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-Sjöstrand 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. |
| title | Wiener pairs of Banach algebras of operator-valued matrices |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2407.16416 |