## Rocky Mountain Journal of Mathematics

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

Maliheh Hosseini

#### 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

#### 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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