Linear Maps Preserving Function Calculus and Entropies

We show that a unital map between Jordan–Banach algebras or Banach algebras that preserves function calculus given by a single nontrivial locally analytic function must be a Jordan morphism. Ramifications of this results are presented. As an application we prove that quantum channel on general Jorda...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024, Vol.45 (6), p.2502-2508
Main Authors: Hamhalter, J., Turilova, E.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Analytic functions
Entropy (Information theory)
Geometry
Homomorphisms
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Summary:We show that a unital map between Jordan–Banach algebras or Banach algebras that preserves function calculus given by a single nontrivial locally analytic function must be a Jordan morphism. Ramifications of this results are presented. As an application we prove that quantum channel on general Jordan -algebras preserving Segal and Renyi entropy must be a Jordan homomorphism.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224603291