Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras
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| Format: | Preprint |
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2025
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| author | Dabhi, Prakash A. Solanki, Karishman B. |
| author_facet | Dabhi, Prakash A. Solanki, Karishman B. |
| contents | We prove that the weighted quasi-Banach algebras of operator valued matrices satisfying Schur and Baskakov-Gohberg-Sjöstrand (BGS) conditions are inverse-closed in the Banach algebra $B(\ell^2(X,\mathcal{H}))$ whenever the weight is admissible, where $\mathcal{H}$ is a Hilbert space and $X$ is a relatively separated subset of $\mathbb{R}^d$. Furthermore, we identify the Gel'fand space of weighted infinite variable group algebra $\ell^p_ω(\mathbb{Z^N})$ for $0<p\leq1$, and establish inverse-closedness of infinite variable analogue of BGS-type algebra in $B(\ell^2(\mathbb{Z^N},\mathcal{H}))$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras Dabhi, Prakash A. Solanki, Karishman B. Functional Analysis Primary: 47A56, 43A15, 46A16, Secondary: 47L30, 46H35, 47C10 We prove that the weighted quasi-Banach algebras of operator valued matrices satisfying Schur and Baskakov-Gohberg-Sjöstrand (BGS) conditions are inverse-closed in the Banach algebra $B(\ell^2(X,\mathcal{H}))$ whenever the weight is admissible, where $\mathcal{H}$ is a Hilbert space and $X$ is a relatively separated subset of $\mathbb{R}^d$. Furthermore, we identify the Gel'fand space of weighted infinite variable group algebra $\ell^p_ω(\mathbb{Z^N})$ for $0<p\leq1$, and establish inverse-closedness of infinite variable analogue of BGS-type algebra in $B(\ell^2(\mathbb{Z^N},\mathcal{H}))$. |
| title | Inverse-closedness of weighted Schur and BGS type quasi-Banach algebras |
| topic | Functional Analysis Primary: 47A56, 43A15, 46A16, Secondary: 47L30, 46H35, 47C10 |
| url | https://arxiv.org/abs/2509.16641 |