Abstract
Let $\alpha _0\in \mathbb {C} \setminus \{0\}$, $A$ and $B$ be Banach function algebras. Also, let $\rho _1:\Omega _1 \rightarrow A$, $\rho _2:\Omega _2 \rightarrow A$, $\tau _1: \Omega _1 \rightarrow B$ and $\tau _2:\Omega _2 \rightarrow B$ be surjections such that $\|\rho _1(\omega _1)\rho _2(\omega _2)+\alpha _0\|_\infty =\|\tau _1(\omega _1)\tau _2(\omega _2)+\alpha _0\|_\infty $ for all $\omega _1\in \Omega _1, \omega _2\in \Omega _2$, where $\Omega _1$, $\Omega _2$ are two non-empty sets. Motivated by recent investigations on such maps between unital Banach function algebras, in this paper we characterize these maps for certain non-unital Banach function algebras including pointed Lipschitz algebras and abstract Segal algebras of the Talamanca-Herz algebras when the underlying groups are first countable. Moreover, sufficient conditions are given to guarantee such maps induce weighted composition operators.
Citation
Maliheh Hosseini. "Nonlinear spectral radius preservers between certain non-unital Banach function algebras." Rocky Mountain J. Math. 48 (3) 859 - 884, 2018. https://doi.org/10.1216/RMJ-2018-48-3-859
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