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Nonlinear maps preserving the pseudo spectral radius of skew semi-triple products of operators

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Abstract

Let H be a complex Hilbert space of dimension greater than 2,and denote by ℒ(H) the algebra of all bounded linear operators on H. For ε > 0 and T 2 L(H), let rε(T) denote the ε-pseudo spectral radius of T. Let G1and G2 be subsets of ℒ(H) which contain all rank one operators and the identity. A characterization is obtained for surjective maps ϕ: G1 → G2 satisfying rε(ϕ(T)ϕ(S) ϕ(T)) = rϕ(T, S ∈G1) (T, S 2 S1). An analogous description is also obtained for the pseudo spectrum of operators.

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Authors and Affiliations

  1. Department of Mathematics, ENSAM, Moulay Ismail University, B.P. 15290, Al Mansour, Meknès, Morocco

    M. Bendaoud & M. Sarih

  2. Department of Mathematics, Faculty of Sciences, Moulay Ismail University, B.P. 11201, Zitoune, Meknès, Morocco

    A. Benyouness

Authors
  1. M. Bendaoud
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  2. A. Benyouness
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  3. M. Sarih
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Corresponding author

Correspondence to M. Bendaoud.

Additional information

Communicated by L. Molnár

This work was partially supported by a grant from MIU-SRA, Morocco.

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Bendaoud, M., Benyouness, A. & Sarih, M. Nonlinear maps preserving the pseudo spectral radius of skew semi-triple products of operators. ActaSci.Math. 84, 39–47 (2018). https://doi.org/10.14232/actasm-017-825-8

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  • DOI: https://doi.org/10.14232/actasm-017-825-8

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