Israel Journal of Mathematics

, Volume 176, Issue 1, pp 363–380

Maps completely preserving idempotents and maps completely preserving square-zero operators

Authors

  • Jinchuan Hou
    • Department of MathematicsTaiyuan University of Technology
    • Department of MathematicsShanxi University
  • Li Huang
    • Department of MathematicsShanxi University
    • Department of MathematicsTaiyuan University of Science and Technology
Article

DOI: 10.1007/s11856-010-0032-y

Cite this article as:
Hou, J. & Huang, L. Isr. J. Math. (2010) 176: 363. doi:10.1007/s11856-010-0032-y
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Abstract

Let X, Y be real or complex Banach spaces with dimension greater than 2 and let A, B be standard operator algebras on X and Y, respectively. In this paper, we show that every map completely preserving idempotence from A onto B is either an isomorphism or (in the complex case) a conjugate isomorphism; every map completely preserving square-zero from A onto B is a scalar multiple of either an isomorphism or (in the complex case) a conjugate isomorphism.

Copyright information

© Hebrew University Magnes Press 2010