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arXiv · 2605.18179

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

Jekwin J. Dabhi·Prakash A. Dabhi
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Abstract

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.

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Jekwin J. Dabhi, Prakash A. Dabhi. 2026-05-18. On Multiplicity of Uniform Norms and Maximal Spectral Substructures in Commutative Banach Algebras. https://arxiv.org/abs/2605.18179

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