Algebraic reflexivity of diameter-preserving linear bijections between $C(X)$-spaces

A. Jiménez-Vargas; Fereshteh Sady

doi:10.5565/PUBLMAT6522110

2021 Algebraic reflexivity of diameter-preserving linear bijections between $C(X)$-spaces

A. Jiménez-Vargas, Fereshteh Sady

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Abstract

We prove that if $X$ and $Y$ are first countable compact Hausdorff spaces, then the set of all diameter-preserving linear bijections from $C(X)$ to $C(Y)$ is algebraically reflexive.

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A. Jiménez-Vargas. Fereshteh Sady. "Algebraic reflexivity of diameter-preserving linear bijections between $C(X)$-spaces." Publ. Mat. 65 (2) 727 - 746, 2021. https://doi.org/10.5565/PUBLMAT6522110

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Received: 31 January 2020; Revised: 1 March 2021; Published: 2021

First available in Project Euclid: 21 June 2021

Digital Object Identifier: 10.5565/PUBLMAT6522110

Subjects:

Primary: 46B04 , 47B38

Keywords: algebraic reflexivity , diameter-preserving map , local linear map , Weighted composition operator

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