Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MAPS PRESERVING GENERALIZED PROJECTION OPERATORS

  • Hassane Benbouziane (Department of Mathematics Faculty of Sciences Dhar El Mahraz University Sidi Mohammed Ben Abdellah) ;
  • Kaddour Chadli (Department of Mathematics Faculty of Sciences Dhar El Mahraz University Sidi Mohammed Ben Abdellah) ;
  • Mustapha Ech-cherif El Kettani (Department of Mathematics Faculty of Sciences Dhar El Mahraz University Sidi Mohammed Ben Abdellah)
  • Received : 2023.12.01
  • Accepted : 2024.05.28
  • Published : 2024.07.31
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Abstract

Let 𝓑(H) be the algebra of all bounded linear operators on a Hilbert space H with dim(H) > 2. Let 𝒢𝒫(H) be the subset of 𝓑(H) of all generalized projection operators. In this paper, we give a complete characterization of surjective maps 𝚽 : 𝓑(H) → 𝓑(H) satisfying A-𝛌B ∈ 𝒢𝒫(H) ⇔ 𝚽(A) - 𝛌𝚽(B) ∈ 𝒢𝒫(H) for any A, B ∈ 𝓑(H) and 𝛌 ∈ ℂ.

Keywords

Acknowledgement

We thank the reviewers for their valuable comments, which improved the paper's presentation.

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