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Acta Mathematica Vietnamica

, Volume 43, Issue 3, pp 575–583 | Cite as

A Generalization of Strongly Preserver Problems of Drazin Invertibility

  • Mourad Oudghiri
  • Khalid Souilah
Article
  • 347 Downloads

Abstract

Let ϕ be an additive map between unital complex Banach algebras such that ϕ(1) is invertible. We show that ϕ satisfies ϕ(aD)ϕ(b)D = ϕ(a)Dϕ(bD) for every Drazin invertible elements a, b if and only if ϕ(1)− 1ϕ is a Jordan homomorphism and ϕ(1) commutes with the range of ϕ. A similar result is established for group invertible elements, and more explicit forms of such maps are given in the context of the algebra of all bounded linear operators on a complex Banach space.

Keywords

Linear preserver problems Jordan homomorphism Drazin invertibility 

Mathematics Subject Classification (2010)

47B48 47B49 47L99 46H05 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Département Math-Info, Labo LAGA, Faculté des SciencesUniversité Mohammed PremierOujdaMorocco

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