Banach algebra mappings preserving the invertibility of linear pencils

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Let A and B be complex unital Banach algebras, and let φ,ψ:A→B be surjective mappings. If A is semisimple with an essential socle and φ and ψ together preserve the invertibility of linear pencils in both directions, that is, for any x,y∈A and λ∈C, λx+y is invertible in A if and only if λφ(x)+ψ(y) is invertible in B, then we show that there exists an invertible element u in B and a Jordan isomorphism J:A→B such that φ(x)=ψ(x)=uJ(x) for all x∈A.

Original languageEnglish
Pages (from-to)109-122
Number of pages14
JournalLinear Algebra and Its Applications
Publication statusPublished - 15 Jun 2024


  • Banach algebra
  • Invertibility preserving mappings
  • Jordan isomorphism
  • Rank
  • Trace

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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