On the BSE- property of vector valued Beurling algebra $L^1(G,ω, \mathcal{A})$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912975463383040 |
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| author | Dabhi, Jekwin Dabhi, Prakash |
| author_facet | Dabhi, Jekwin Dabhi, Prakash |
| contents | Let $G$ be a locally compact abelian group, and let $ω:G \to [1,\infty)$ be a measurable weight, i.e., $ω$ is measurable, and $ω(s+t)\leq ω(s)ω(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative Banach algebra with a predual $\mathcal A_\ast$ such that the Gel'fand space $Φ_{\mathcal A}\subset \mathcal{A}_\ast$. If $ω^{-1}$ is vanishing at infinity, then we show that the Banach algebra $L^1(G,ω,\mathcal{A})$ is a BSE- algebra if and only if $\mathcal A$ is a BSE- algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19645 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the BSE- property of vector valued Beurling algebra $L^1(G,ω, \mathcal{A})$ Dabhi, Jekwin Dabhi, Prakash Functional Analysis Primary 46J05, 46J10, 43A25 Let $G$ be a locally compact abelian group, and let $ω:G \to [1,\infty)$ be a measurable weight, i.e., $ω$ is measurable, and $ω(s+t)\leq ω(s)ω(t)$ for all $s, t \in G$. Let $\mathcal{A}$ be a semisimple commutative Banach algebra with a predual $\mathcal A_\ast$ such that the Gel'fand space $Φ_{\mathcal A}\subset \mathcal{A}_\ast$. If $ω^{-1}$ is vanishing at infinity, then we show that the Banach algebra $L^1(G,ω,\mathcal{A})$ is a BSE- algebra if and only if $\mathcal A$ is a BSE- algebra. |
| title | On the BSE- property of vector valued Beurling algebra $L^1(G,ω, \mathcal{A})$ |
| topic | Functional Analysis Primary 46J05, 46J10, 43A25 |
| url | https://arxiv.org/abs/2603.19645 |