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3. Maps on self-adjoint operators preserving numerical range of products up to a factorKan He, Jin Chuan Hou, Gregor Dolinar, Bojan Kuzma, 2011, original scientific article Abstract: Let ▫$H$▫ be a complex Hilbert space and ▫${mathscr{S}}_a(H)$▫ the space of all self adjoint operators on ▫$H$▫. ▫$Phi colon {mathscr{S}}_a(H) to {mathscr{S}}_a(H)$▫ is a surjective map. For ▫$xi, eta in mathbb{C} setminus {1}$▫, then ▫$Phi$▫ satisfies that ▫$$W(AB - xi BA) = W(Phi(A)Phi(B) - etaPhi(B)phi(A))$$▫ for all ▫$A,B in {mathscr{S}}_a(H)$▫ if and only if there exists a unitary operator or con-unitary operator ▫$U$▫ such that ▫$Phi(A) = UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫ or ▫$Phi(A) = -UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫.
Keywords: matematika, teorija operatorjev, numerični zaklad, ohranjevalci
Published in RUP: 03.04.2017; Views: 2321; Downloads: 32
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5. Beasley, Leroy B.; Guterman, Alexander E.; Jun, Young-Bae; Song, Seok-Zun: Linear preservers of extremes of rank inequalities over semirings: Row and column ranks. (English). - [J] Linear Algebra Appl. 413, No. 2-3, 495-509 (2006). [ISSN 0024-3795]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, lnearni ohranjevalci, polkolobar
Published in RUP: 15.10.2013; Views: 2497; Downloads: 34
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6. Purificação Coelho, M.; Duffner, M.Antónia: Immanant preserving and immanant converting maps. (English). - [J] Linear Algebra Appl. 418, No. 1, 177-187 (2006). [ISSN 0024-3795]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, linearne transformacije, ohranjevalci
Published in RUP: 15.10.2013; Views: 2771; Downloads: 35
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8. Tang, Xiao-Ming; Cao, Chong-Guang: Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications. (English). - [J] J. Appl. Math. Comput. 19, No. 1-2, 253-260 (2005). [ISSN 1598-5865]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linearna algebra, ohranjevalci, hermitska matrika, adjungirana matrika, jordanski homomorfizem
Published in RUP: 15.10.2013; Views: 2188; Downloads: 34
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9. Ob otobraženijah, sohranjajuščih immanantyBojan Kuzma, 2007, original scientific article Abstract: V članku študiramo preslikave, ki transformirajo eno imananto matričnih snopov v drugo. Vnaprej ne predpostavimo niti surjektivnosti, niti linearnosti preslikav. Predpostavimo zgolj šibko linearnost v obliki identitete ▫$d_chi (Phi(A) + lambda Phi(B)) = d_{chi'}(A+lambda B)$▫. Pokažemo, da zgolj ta identiteta implicira avtomatično linearnost in bijektivnost preslikave ▫$Phi$▫.
Keywords: matematika, linearna algebra, teorija matrik, imanante, ohranjevalci
Published in RUP: 15.10.2013; Views: 2841; Downloads: 90
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