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1.
Linear maps preserving numerical radius of tensor products of matrices
Ajda 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.
Found in: osebi
Keywords: matematika, teorija matrik, kompleksne matrike, linearni ohranjevalci, numerični rang, numerični radij, tenzorski produkt
Published: 15.10.2013; Views: 1901; Downloads: 37
URL Full text (0,00 KB)

2.
Norm preservers of Jordan products
Bojan 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.
Found in: osebi
Keywords: matematika, linearna algebra, jordanski produkt, matrična norma, ohranjevalci
Published: 15.10.2013; Views: 1404; Downloads: 59
URL Full text (0,00 KB)
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3.
Tracial numerical ranges and linear dependence of operators
Bojan 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.
Found in: osebi
Keywords: matematika, linearna algebra, teorija operatorjev, Hilbertov prostor, linearni operatorji, linearna odvisnost, posplošen numerični zaklad
Published: 15.10.2013; Views: 1647; Downloads: 55
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4.
Mappings that preserve pairs of operators with zero triple Jordan product
Gorazd Lešnjak, Tatjana Petek, Chi-Kwong Li, Bojan Kuzma, Mirko Dobovišek, 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.
Found in: osebi
Keywords: matrix algebra, Jordan triple product, nonlinear preservers
Published: 03.04.2017; Views: 716; Downloads: 34
URL Full text (0,00 KB)

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