{"title":"算子值矩阵的巴拿赫代数的维纳对","authors":"Lukas Köhldorfer, Peter Balazs","doi":"arxiv-2407.16416","DOIUrl":null,"url":null,"abstract":"In this article we introduce several new examples of Wiener pairs\n$\\mathcal{A} \\subseteq \\mathcal{B}$, where $\\mathcal{B} =\n\\mathcal{B}(\\ell^2(X;\\mathcal{H}))$ is the Banach algebra of bounded operators\nacting on the Hilbert space-valued Bochner sequence space\n$\\ell^2(X;\\mathcal{H})$ and $\\mathcal{A} = \\mathcal{A}(X)$ is a Banach algebra\nconsisting of operator-valued matrices indexed by some relatively separated set\n$X \\subset \\mathbb{R}^d$. In particular, we introduce\n$\\mathcal{B}(\\mathcal{H})$-valued versions of the Jaffard algebra, of certain\nweighted Schur-type algebras, of Banach algebras which are defined by more\ngeneral off-diagonal decay conditions than polynomial decay, of weighted\nversions of the Baskakov-Gohberg-Sj\\\"ostrand algebra, and of anisotropic\nvariations of all of these matrix algebras, and show that they are\ninverse-closed in $\\mathcal{B}(\\ell^2(X;\\mathcal{H}))$. In addition, we obtain\nthat each of these Banach algebras is symmetric.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wiener pairs of Banach algebras of operator-valued matrices\",\"authors\":\"Lukas Köhldorfer, Peter Balazs\",\"doi\":\"arxiv-2407.16416\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article we introduce several new examples of Wiener pairs\\n$\\\\mathcal{A} \\\\subseteq \\\\mathcal{B}$, where $\\\\mathcal{B} =\\n\\\\mathcal{B}(\\\\ell^2(X;\\\\mathcal{H}))$ is the Banach algebra of bounded operators\\nacting on the Hilbert space-valued Bochner sequence space\\n$\\\\ell^2(X;\\\\mathcal{H})$ and $\\\\mathcal{A} = \\\\mathcal{A}(X)$ is a Banach algebra\\nconsisting of operator-valued matrices indexed by some relatively separated set\\n$X \\\\subset \\\\mathbb{R}^d$. In particular, we introduce\\n$\\\\mathcal{B}(\\\\mathcal{H})$-valued versions of the Jaffard algebra, of certain\\nweighted Schur-type algebras, of Banach algebras which are defined by more\\ngeneral off-diagonal decay conditions than polynomial decay, of weighted\\nversions of the Baskakov-Gohberg-Sj\\\\\\\"ostrand algebra, and of anisotropic\\nvariations of all of these matrix algebras, and show that they are\\ninverse-closed in $\\\\mathcal{B}(\\\\ell^2(X;\\\\mathcal{H}))$. In addition, we obtain\\nthat each of these Banach algebras is symmetric.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.16416\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.16416","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.