20.500.12556/RUP-765 Norm preservers of Jordan products 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. 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. matematika linearna algebra jordanski produkt matrična norma ohranjevalci mathematics linear algebra Jordan product matrix norm nonlinear preservers true true false Angleški jezik Neznan jezik Delo ni kategorizirano 2013-10-15 12:05:10 2013-10-15 12:05:10 2024-03-01 11:58:53 0000-00-00 00:00:00 2011 0 0 str. 959-978 Vol. 22 2011 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1081-3810 512.643 16068441 http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol22_pp959-978.pdf 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=765 Inštitut Andrej Marušič 0 0 0