Title

Norm Preservers of Jordan Products

Document Type

Article

Department/Program

Mathematics

Journal Title

Electronic Journal of Linear Algebra

Pub Date

2011

Volume

22

First Page

959

Abstract

Norm preserver maps of Jordan product on the algebra M(n) of n x n complex matrices are studied, with respect to various norms. A description of such surjective maps with respect to the Frobenius norm is obtained: Up to a suitable scaling and unitary similarity, they are given by one of the four standard maps (identity, transposition, complex conjugation, and conjugate transposition) on M(n), except for a set of normal matrices; on the exceptional set they are given by another standard map. For many other norms, it is proved that, after a suitable reduction, norm preserver maps of Jordan product transform every normal matrix to its scalar multiple, or to a scalar multiple of its conjugate transpose.

DOI

10.13001/1081-3810.1484

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