Linear maps preserving G-quasi-isometry operators

Abstract

Let \({\mathscr {H}}\) be a complex Hilbert space and \({\mathscr {B}}({\mathscr {H}})\) the algebra of all bounded linear operators on \({\mathscr {H}}\). We give the concrete forms of surjective continue unital linear maps from \({\mathscr {B}}({\mathscr {H}})\) onto itself that preserves G-quasi-isometric operators.

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Correspondence to Iz-iddine EL-Fassi.

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Chahbi, A., EL-Fassi, I. & Kabbaj, S. Linear maps preserving G-quasi-isometry operators. Bol. Soc. Mat. Mex. 26, 37–43 (2020). https://doi.org/10.1007/s40590-019-00238-2

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Keywords

  • Linear preserver
  • Jordan homomorphisms
  • Operators on spaces with an indefinite metric
  • Partial-isometry operators

Mathematics Subject Classification

  • Primary 15A86
  • 15A04
  • 47B50
  • Secondary 47L30
  • 16W20