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Maps Preserving the Numerical Radius Distance Between \(C^*\)-Algebras

  • Abdellatif BourhimEmail author
  • Mohamed Mabrouk
Article
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Abstract

Let \(\mathscr {A}\) and \(\mathscr {B}\) be unital \(C^*\)-algebras, and let v(a) be the numerical radius of any element \(a\in \mathscr {A}\). We show that if a map T from \(\mathscr {A}\) onto \(\mathscr {B}\) satisfies \(v(T(a)-T(b))=v(a-b),~~(a,~ b\in \mathscr {A}),\) then \(T(\mathbf{1 })-T(0)\) is a unitary central element in \(\mathscr {B}\). This shows that the characterization of Bai, Hou and Xu for the numerical radius distance preservers on \(C^*\)-algebras can be obtained without the extra condition that \(T(\mathbf{1 })-T(0)\) is in the center of \(\mathscr {B}\).

Keywords

\(C^*\)-algebras Isometry Numerical range Numerical radius Numerical range and radius preservers 

Mathematics Subject Classification

Primary 15A86 46L05 Secondary 15A60 47A12 47B49 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of Mathematics, Faculty of Applied SciencesUmm Al-Qura UniversityMakkahSaudi Arabia
  3. 3.Department of Mathematics, Faculty of Sciences of SfaxUniversity of SfaxSfaxTunisia

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