Acta Mathematica Sinica

, Volume 20, Issue 4, pp 761–768 | Cite as

A Characterization of Homomorphisms Between Banach Algebras

ORIGINAL ARTICLES

Abstract

We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism; this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras. For a unital linear map Φ from a semi-simple complex Banach algebra onto another, we also show that the following statements are equivalent: (1) Φ is an homomorphism; (2) Φ is completely invertibility preserving; (3) Φ is 2-invertibility preserving.

Keywords

Banach algebras Homomorphisms Jordan homomorphisms 

MR (2000) Subject Classification

46L10 47B48 47B49 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijing 100871P. R. China
  2. 2.Department of Applied MathematicsTaiyuan University of TechnologyTaiyuan 030024P. R. China
  3. 3.Department of MathematicsShanxi Teachers UniversityLinfen 041004P. R. China
  4. 4.Department of MathematicsShanxi UniversityTaiyuan 030000P. R. China

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