A note on a question of Garth Dales: Arens regularity as a three space property
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914180558225408 |
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| author | Filali, Mahmoud Galindo, Jorge |
| author_facet | Filali, Mahmoud Galindo, Jorge |
| contents | Garth Dales asked whether a Banach algebra $\mathcal{A}$ having an Arens regular closed ideal $\mathcal{J}$ with Arens regular quotient $\mathcal{A}/\mathcal{J}$ is necessarily Arens regular. We prove in this note that, for a class of Banach algebras including the standard algebras in harmonic analysis, Garth's conditions force the algebra to be even reflexive. We also give examples of Banach algebras with Garth's conditions, that are not Arens regular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_09947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on a question of Garth Dales: Arens regularity as a three space property Filali, Mahmoud Galindo, Jorge Functional Analysis 22D15, 43A46, 43A60, 47C15 Garth Dales asked whether a Banach algebra $\mathcal{A}$ having an Arens regular closed ideal $\mathcal{J}$ with Arens regular quotient $\mathcal{A}/\mathcal{J}$ is necessarily Arens regular. We prove in this note that, for a class of Banach algebras including the standard algebras in harmonic analysis, Garth's conditions force the algebra to be even reflexive. We also give examples of Banach algebras with Garth's conditions, that are not Arens regular. |
| title | A note on a question of Garth Dales: Arens regularity as a three space property |
| topic | Functional Analysis 22D15, 43A46, 43A60, 47C15 |
| url | https://arxiv.org/abs/2407.09947 |