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Maps completely preserving commutativity and maps completely preserving Jordan zero-product

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Identifiers
DOI: 10.1016/j.laa.2014.08.016
Keywords
  • Standard Operator Algebras
  • Completely Preserver Problems
  • Commutativity
  • Jordan Zero-Product
  • Isomorphisms
Disciplines
  • Mathematics

Abstract

Abstract Let X, Y be real or complex Banach spaces with infinite dimension, and let A, B be standard operator algebras on X and Y, respectively. In this paper, we show that every map completely preserving commutativity from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism. Every map completely preserving Jordan zero-product from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.

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