Israel Journal of Mathematics

, Volume 176, Issue 1, pp 363–380

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

  • Jinchuan Hou
  • Li Huang

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


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

Authors and Affiliations

  • Jinchuan Hou
    • 1
    • 2
  • Li Huang
    • 2
    • 3
  1. 1.Department of MathematicsTaiyuan University of TechnologyTaiyuanP. R. China
  2. 2.Department of MathematicsShanxi UniversityTaiyuanP. R. China
  3. 3.Department of MathematicsTaiyuan University of Science and TechnologyTaiyuanP. R. China