On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras

Fuente: arXiv
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Hauptverfasser: Dabhi, Jekwin J., Dabhi, Prakash A.
Format: Preprint
Veröffentlicht: 2026
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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