Integral Equations and Operator Theory

, Volume 55, Issue 1, pp 93–109

Linear Maps Preserving Generalized Invertibility

Original Paper

DOI: 10.1007/s00020-006-1421-9

Cite this article as:
Mbekhta, M., Rodman, L. & Šemrl, P. Integr. equ. oper. theory (2006) 55: 93. doi:10.1007/s00020-006-1421-9
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Abstract.

Let H be an infinite-dimensional complex separable Hilbert space and \( \mathcal{B}(H) \) the algebra of all bounded linear operators on H. Let \( \phi :\mathcal{B}(H) \to \mathcal{B}(H) \) be a bijective continuous unital linear map preserving generalized invertibility in both directions. Then the ideal of all compact operators is invariant under ϕ and the induced linear map on the Calkin algebra is either an automorphism or an antiautomorphism.

Mathematics Subject Classification (2000).

47B49 47L99 

Keywords.

Generalized invertibility linear preservers Calkin algebra 

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.UFR de MathématiquesUniversité de Lille IVilleneuve d’Ascq Cedex, LilleFrance
  2. 2.Department of MathematicsThe College of William and MaryWilliamsburgUSA
  3. 3.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia

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