Jekwin J. Dabhi | Searcharxiv

arXiv2026

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

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.

math.FA↗

arXiv2026

On the BSE and BED properties of the Beurling algebra $L^1(G,ω)$

Let $G$ be a locally compact abelian group, and let $ω:G \to [1,\infty)$ be a weight, i.e., $ω$ is measurable, $ω$ is locally bounded and $ω(s+t)\leq ω(s)ω(t)$ for all $s, t \in G$. If $ω^{-1}$ is vanishing at infinity, then we show that the Beurling algebra $L^1(G,ω)$ is both BSE- algebra and BED- algebra.

math.FA↗