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2018 Nonlinear spectral radius preservers between certain non-unital Banach function algebras
Maliheh Hosseini
Rocky Mountain J. Math. 48(3): 859-884 (2018). DOI: 10.1216/RMJ-2018-48-3-859

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

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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

Information

Published: 2018
First available in Project Euclid: 2 August 2018

zbMATH: 06917351
MathSciNet: MR3835576
Digital Object Identifier: 10.1216/RMJ-2018-48-3-859

Subjects:
Primary: 46J10, 47B48
Secondary: 47B33

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 3 • 2018
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