Rocky Mountain Journal of Mathematics

Nonlinear spectral radius preservers between certain non-unital Banach function algebras

Maliheh Hosseini

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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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 3 (2018), 859-884.

Dates
First available in Project Euclid: 2 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1533230829

Digital Object Identifier
doi:10.1216/RMJ-2018-48-3-859

Mathematical Reviews number (MathSciNet)
MR3835576

Zentralblatt MATH identifier
06917351

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 47B48: Operators on Banach algebras
Secondary: 47B33: Composition operators

Keywords
Banach function algebra norm-preserving map peripheral range Figà-Talamanca-Herz algebra Figà-Talamanca-Herz-Lebesgue algebra Lipschitz algebra

Citation

Hosseini, Maliheh. Nonlinear spectral radius preservers between certain non-unital Banach function algebras. Rocky Mountain J. Math. 48 (2018), no. 3, 859--884. doi:10.1216/RMJ-2018-48-3-859. https://projecteuclid.org/euclid.rmjm/1533230829


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