Acta Mathematica Sinica

, Volume 20, Issue 4, pp 761–768

A Characterization of Homomorphisms Between Banach Algebras


    • School of Mathematical SciencesPeking University
    • Department of Applied MathematicsTaiyuan University of Technology
  • Jin Chuan Hou
    • Department of MathematicsShanxi Teachers University
    • Department of MathematicsShanxi University

DOI: 10.1007/s10114-004-0312-8

Cite this article as:
Cui, J.L. & Hou, J.C. Acta Math Sinica (2004) 20: 761. doi:10.1007/s10114-004-0312-8


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.


Banach algebrasHomomorphismsJordan homomorphisms

MR (2000) Subject Classification

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© Springer-Verlag Berlin Heidelberg 2004