On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914577627742208 |
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| author | Dabhi, Jekwin J. Dabhi, Prakash A. |
| author_facet | Dabhi, Jekwin J. Dabhi, Prakash A. |
| contents | Let $\mathcal A$ be a semisimple commutative Banach algebra. It is shown that either $\mathcal A$ has exactly one uniform norm or it admits uncountably many uniform norms. Further, it is shown that there always exists a largest closed subalgebra of $\mathcal A$ which is weakly regular, and that there always exist largest closed ideals in $\mathcal A$ having unique uniform norm property (UUNP) and spectral extension property (SEP) respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18179 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras Dabhi, Jekwin J. Dabhi, Prakash A. Functional Analysis Primary 46J05, 46J40 Let $\mathcal A$ be a semisimple commutative Banach algebra. It is shown that either $\mathcal A$ has exactly one uniform norm or it admits uncountably many uniform norms. Further, it is shown that there always exists a largest closed subalgebra of $\mathcal A$ which is weakly regular, and that there always exist largest closed ideals in $\mathcal A$ having unique uniform norm property (UUNP) and spectral extension property (SEP) respectively. |
| title | On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras |
| topic | Functional Analysis Primary 46J05, 46J40 |
| url | https://arxiv.org/abs/2605.18179 |