Functional identities and zero Lie product determined Banach algebras

TL;DR

This paper explores the relationship between functional identities and zero Lie product determined Banach algebras, focusing on commuting maps, derivations, and bijective commutativity-preserving maps.

Contribution

It introduces new connections between functional identities and zero Lie product determined Banach algebras, addressing three specific problems in the area.

Findings

Characterization of commuting linear maps

Analysis of derivations preserving commutativity

Description of bijective commutativity-preserving linear maps

Abstract

Three problems connecting functional identities to the recently introduced notion of a zero Lie product determined Banach algebra are discussed. The first one concerns commuting linear maps, the second one concerns derivations that preserve commutativity, and the third one concerns bijective commutativity preserving linear maps.