1. Mappings that preserve pairs of operators with zero triple Jordan productMirko Dobovišek, Bojan Kuzma, Gorazd Lešnjak, Chi-Kwong Li, Tatjana Petek, 2007, original scientific article Abstract: 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. Keywords: matrix algebra, Jordan triple product, nonlinear preservers Published in RUP: 03.04.2017; Views: 2428; Downloads: 97 Link to full text |
2. Tracial numerical ranges and linear dependence of operatorsBojan Kuzma, Chi-Kwong Li, Leiba Rodman, 2011, original scientific article Abstract: Pokazano je, da lahko linearno odvisnost dveh operatorjev na Hilbertovem prostoru preverimo s pomočjo identičnosti v modulu dane sesquilinearne oz. kvadratične forme, pridružene operatorjema. Forme so bazirane na posplošenih numeričnih zakladih. Keywords: matematika, linearna algebra, teorija operatorjev, Hilbertov prostor, linearni operatorji, linearna odvisnost, posplošen numerični zaklad Published in RUP: 15.10.2013; Views: 3769; Downloads: 230 Link to full text |
3. Norm preservers of Jordan productsBojan Kuzma, Gorazd Lešnjak, Chi-Kwong Li, Tatjana Petek, Leiba Rodman, 2011, original scientific article 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 Published in RUP: 15.10.2013; Views: 3234; Downloads: 227 Link to full text |
4. Linear maps preserving numerical radius of tensor products of matricesAjda Fošner, Zejun Huang, Chi-Kwong Li, Nung-Sing Sze, 2013, original scientific article Abstract: V članku so karakterizirane linearne preslikave na tenzorskem produktu kompleksnih matrik, ki ohranjajo numerični radij. Keywords: matematika, teorija matrik, kompleksne matrike, linearni ohranjevalci, numerični rang, numerični radij, tenzorski produkt Published in RUP: 15.10.2013; Views: 4666; Downloads: 102 Link to full text |