Surjective maps preserving the reduced minimum modulus of products

Sepide Hajighasemi; Shirin Hejazian

doi:10.56754/0719-0646.2501.139

Authors

Sepide Hajighasemi Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran. https://orcid.org/0000-0001-6615-9979
Shirin Hejazian Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran. https://orcid.org/0000-0003-3052-1862

DOI:

https://doi.org/10.56754/0719-0646.2501.139

Keywords:

Reduced minimum modulus, operator product, Jordan triple product, nonlinear preservers

Abstract

Suppose \(\mathfrak{B}(H)\) is the Banach algebra of all bounded linear operators on a Hilbert space \(H\) with \(\dim(H)\geq 3\). Let \(\gamma(.)\) denote the reduced minimum modulus of an operator. We charaterize surjective maps \(\varphi\) on \(\mathfrak{B}(H)\) satisfying

\(\gamma(\varphi(T)\varphi(S))=\gamma(T S)\;\;\;(T, S\in \mathfrak{B}(H)).\)

Also, we give the general form of surjective maps on \(\mathfrak B(H)\) preserving the reduced minimum modulus of Jordan triple products of operators.

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