Geodesic
Norm preservers of Jordan products
The electronic journal of linear algebra, Tome 22 (2011), pp. 959-978.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Norm preserver maps of Jordan product on the algebra M n of n$\times n$ 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.
Classification : 15A60, 15A86, 15A30
Keywords: Jordan product, matrix norm, nonlinear preservers 
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Kuzma, Bojan; Lesnjak, Gorazd; Li, Chi-Kwong; Petek, Tatjana; Rodman, Leiba. Norm preservers of Jordan products. The electronic journal of linear algebra, Tome 22 (2011), pp. 959-978. http://geodesic.mathdoc.fr/item/ELA_2011__22__a15/