Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures
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| Format: | Preprint |
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2025
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| _version_ | 1866911061345566720 |
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| author | Dabra, Arvish Kumar, N. Shravan |
| author_facet | Dabra, Arvish Kumar, N. Shravan |
| contents | In this article, we study the isomorphism problem for the algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures, denoted by $PF_Φ(G)$ and $PM_Φ(G),$ respectively. More precisely, for a certain class of Young functions $Φ,$ we prove that if there exists an isometric isomorphism between $PF_Φ(G_1)$ and $PF_Φ(G_2),$ or between $PM_Φ(G_1)$ and $PM_Φ(G_2),$ then $G_1$ and $G_2$ are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott's theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_13020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures Dabra, Arvish Kumar, N. Shravan Functional Analysis Primary 46E30, 43A22, Secondary 43A15 In this article, we study the isomorphism problem for the algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures, denoted by $PF_Φ(G)$ and $PM_Φ(G),$ respectively. More precisely, for a certain class of Young functions $Φ,$ we prove that if there exists an isometric isomorphism between $PF_Φ(G_1)$ and $PF_Φ(G_2),$ or between $PM_Φ(G_1)$ and $PM_Φ(G_2),$ then $G_1$ and $G_2$ are isomorphic as topological groups. In addition, we present an Orlicz version of Parrott's theorem. |
| title | Isomorphism Theorems for the Algebras of $Φ-$Pseudofunctions and $Φ-$Pseudomeasures |
| topic | Functional Analysis Primary 46E30, 43A22, Secondary 43A15 |
| url | https://arxiv.org/abs/2507.13020 |