Bojan Kuzma (Author), Gorazd Lešnjak (Author), Chi-Kwong Li (Author), Tatjana Petek (Author), Leiba Rodman (Author)

Abstract

V članku klasificiramo surjektivne preslikave, ki na algebri kompleksnih matrik ohranjajo Frobeniusovo normo Jordanskega produkta. Izkaže se, da so do unitarne podobnosti in množenja s skalarnim večkratnikom vse tovrstne preslikave le štirih možnih tipov: (i) preslikava, ki je lokalno adjungiranje na normalnih matrikah in identiteta izven normalnih matrik, (ii) transponiranje, (iii) kompleksna konjugacija in (iv) adjungiranje. Do podobnih zaključkov pridemo tudi v primeru nekaterih drugih unitarno invariantnih norm, kjer pokažemo, da preslikava bodisi normalne matrike množi s skalarji, bodisi jih adjungira in množi s skalarji.

Keywords

matematika;linearna algebra;jordanski produkt;matrična norma;ohranjevalci;mathematics;linear algebra;Jordan product;matrix norm;nonlinear preservers;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FERI - Faculty of Electrical Engineering and Computer Science
UDC: 512.643
COBISS: 16068441 Link will open in a new window
ISSN: 1081-3810
Views: 3078
Downloads: 227
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Other data

Secondary language: Unknown
Secondary title: Preslikave, ki ohranjajo normo jordanskega produkta
Secondary abstract: 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.
Secondary keywords: mathematics;linear algebra;Jordan product;matrix norm;nonlinear preservers;
Type (COBISS): Not categorized
Pages: str. 959-978
Issue: ǂVol. ǂ22
Chronology: 2011
ID: 68924