Abstract
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 language | English |
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Pages (from-to) | 109-122 |
Number of pages | 14 |
Journal | Linear Algebra and Its Applications |
Volume | 691 |
DOIs | |
Publication status | Published - 15 Jun 2024 |
Keywords
- 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