20.500.12556/RUP-7714 Mappings that preserve pairs of operators with zero triple Jordan product Preslikave, ki ohranjajo ničle produkta Jordanskih trojic Let ▫$\mathbb{F}$▫ be a field and ▫$n \ge 3$▫. Suppose ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})▫$ contain all rank-one idempotents. The structure of surjections ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ satisfying ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫ is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space, (b) the space of Hermitian matrices acting on ▫$n$▫-dimensional vectors over a skew-field, (c) subsets of self-adjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings ▫$\phi$▫ on matrices or operators such that ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))▫$ for all ▫$A,B$▫ for functions ▫$F$▫ such as the spectral norm, Schatten ▫$p$▫-norm, numerical radius and numerical range, etc. Bodi ▫$\mathbb{F}$▫ komutativni obseg in ▫$n \ge 3$▫. Denimo, da ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})$▫ vsebuje vsaj vse idempotente ranga ena. V članku klasificiramo surjekcije ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ z lastnostjo ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫. Klasificiramo tudi sorodne preslikave na (a) podmnožicah omejenih operatorjev na Banachovem prostoru, (b) podmnožicah Hermitskih matrik s koeficienti iz (nenujno komutativnega) obsega, (c) podmnožicah sebi-adjungiranih operatorjev na neskončnorazsežnem, kompleksnem Hilbertovem prostoru. Dobljene rezultate lahko apliciramo npr. pri iskanju preslikav ▫$\phi$▫, z lastnostjo ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))$▫ kjer se ▫$F$▫ unitarno-podobnostno-invariantne funkcije, kot npr. spektralna norma, Schattenova ▫$p$▫-norma, numerični zaklad, numerični radij, itd. matrix algebra Jordan triple product nonlinear preservers matematika matrična algebra produkt jordanskih trojic nelinearni ohranjevalci true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2016-04-08 16:41:27 2017-04-03 08:14:22 2024-03-01 13:33:22 0000-00-00 00:00:00 2007 0 0 str. 255-279 iss. 2-3 Vol. 426 2007 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0024-3795 512.552 1119247 11598870 http://dx.doi.org/10.1016/j.laa.2007.04.017 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7714 Inštitut Andrej Marušič 0 0 0