Arens regularity of the Orlicz Figà-Talamanca Herz Algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909089271906304 |
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| author | Dabra, Arvish Kumar, N. Shravan |
| author_facet | Dabra, Arvish Kumar, N. Shravan |
| contents | Let G be a locally compact group and let $A_Φ(G)$ be the Orlicz-version of the Figà-Talamanca Herz algebra of G associated with a Young function $Φ.$ We show that if $A_Φ(G)$ is Arens regular, then $G$ is discrete. We further explore the Arens regularity of $A_Φ(G)$ when the underlying group $G$ is discrete. In the running, we also show that $A_Φ(G)$ is finite-dimensional if and only if $G$ is finite. Further, for amenable groups, we show that $A_Φ(G)$ is reflexive if and only if $G$ is finite, under the assumption that the associated Young function $Φ$ satisfies the MA-condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17673 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arens regularity of the Orlicz Figà-Talamanca Herz Algebra Dabra, Arvish Kumar, N. Shravan Functional Analysis Primary 43A15, 43A30, 46B22, Secondary 43A60, 46J10 Let G be a locally compact group and let $A_Φ(G)$ be the Orlicz-version of the Figà-Talamanca Herz algebra of G associated with a Young function $Φ.$ We show that if $A_Φ(G)$ is Arens regular, then $G$ is discrete. We further explore the Arens regularity of $A_Φ(G)$ when the underlying group $G$ is discrete. In the running, we also show that $A_Φ(G)$ is finite-dimensional if and only if $G$ is finite. Further, for amenable groups, we show that $A_Φ(G)$ is reflexive if and only if $G$ is finite, under the assumption that the associated Young function $Φ$ satisfies the MA-condition. |
| title | Arens regularity of the Orlicz Figà-Talamanca Herz Algebra |
| topic | Functional Analysis Primary 43A15, 43A30, 46B22, Secondary 43A60, 46J10 |
| url | https://arxiv.org/abs/2401.17673 |