Non-linear modular Birkhoff-James orthogonality preservers between spaces of continuous functions

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Abstract

A new notion of non-linear isomorphisms between Banach modules is introduced based on modular Birkhoff-James orthogonality. It is shown that a (possibly non-linear) bijective modular Birkhoff-James orthogonality preserver in both direction between spaces of continuous functions (vanishing at infinity) induces a homeomorphism between underlying locally compact Hausdorff spaces. Moreover, characterizations of linear and additive modular Birkhoff-James orthogonality preservers between spaces of continuous functions are also given in terms of the induced homeomorphisms and continuous functions having constant absolute values.

Original languageEnglish
Article number124744
JournalJournal of Mathematical Analysis and Applications
Volume495
Issue number2
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • (Modular) Birkhoff-James orthogonality
  • Continuous function
  • Locally compact Hausdorff space
  • Non-linear isomorphism

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