On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910787077931008 |
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| author | Köhldorfer, Lukas Balazs, Peter |
| author_facet | Köhldorfer, Lukas Balazs, Peter |
| contents | We give a self-contained proof of a recently established $\mathcal{B}(\mathcal{H})$-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of $\mathcal{B}(\mathcal{H})$-valued matrices, whose operator norms of their respective entries decay polynomially off the diagonal, is a Banach algebra which is inverse-closed in the Banach algebra $\mathcal{B}(\ell^2(X;\mathcal{H}))$ of all bounded linear operators on $\ell^2(X;\mathcal{H})$, the Bochner-space of square-summable $\mathcal{H}$-valued sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay Köhldorfer, Lukas Balazs, Peter Functional Analysis Operator Algebras We give a self-contained proof of a recently established $\mathcal{B}(\mathcal{H})$-valued version of Jaffards Lemma. That is, we show that the Jaffard algebra of $\mathcal{B}(\mathcal{H})$-valued matrices, whose operator norms of their respective entries decay polynomially off the diagonal, is a Banach algebra which is inverse-closed in the Banach algebra $\mathcal{B}(\ell^2(X;\mathcal{H}))$ of all bounded linear operators on $\ell^2(X;\mathcal{H})$, the Bochner-space of square-summable $\mathcal{H}$-valued sequences. |
| title | On the inverse-closedness of operator-valued matrices with polynomial off-diagonal decay |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2501.09603 |