1. 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: 2320; Downloads: 32
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2. Li, Jinxiu: Applications of Wigner's theorem to positive maps preserving norm of operator products. (English). - [J] J. Math. Study 37, No. 1, 11-16 (2004). [ISSN 1006-6837]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, Wignerjev izrek, operatorska algebra, norma, singularna vrednost
Published in RUP: 15.10.2013; Views: 3506; Downloads: 40
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3. Cui, Jianlian; Hou, Jinchuan: Linear maps preserving idempotence on nest algebras. (English). - [J] Acta Math. Sin., Engl. Ser. 20, No. 5, 807-820 (2004). [ISSN 1439-8516; ISSN 1439-7617]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, idempotentni operatorji, jordanski izomorfizmi
Published in RUP: 15.10.2013; Views: 4146; Downloads: 33
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4. Di, Qinghui; Du, Xuefeng; Hou, Jinchuan. - Adjacency preserving maps on the space of self-adjoint operators. (English). - [J] Chin. Ann. Math., Ser. B 26, No.2, 305-314 (2005). [ISSN 0252-9599; ISSN 1860-6261]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, sebi adjungirani operatorji, sosednost, nelinearne preslikave
Published in RUP: 15.10.2013; Views: 2704; Downloads: 38
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5. Hou, Jinchuan; Zhao, Liankuo: Zero-product preserving additive maps on symmetric operator spaces and self-adjoint operator spaces. (English). - [J] Linear Algebra Appl. 399, 235-244 (2005). [ISSN 0024-3795]Bojan Kuzma, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, simetrični operatorji, sebi adjungirani operatorji, ohranjevalec ničelnega produkta
Published in RUP: 15.10.2013; Views: 3556; Downloads: 28
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6. Uskova, N.B.: On a result of R. Turner. (English. Russian original). - [J] Math. Notes 76, No. 6, 844-854 (2004); translation from Mat. Zametki 76, No. 6, 844-854 (2004). [ISSN 0001-4346; ISSN 1573-8876]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, perturbiran kompakten operator, diagonalizacija kompaktnih operatorjev, Banachov prostor, separabilen Hilbertov prostor
Published in RUP: 15.10.2013; Views: 3520; Downloads: 24
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7. Petek, Tatjana: A note on unitary similarity preserving linear mappings on $B(H)$. (English). - [J] Linear Algebra Appl. 394, 217-224 (2005). [ISSN 0024-3795]Bojan Kuzma, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, simetrični operatorji, Hilbertov prostor, ohranjevalec unitarne podobnosti
Published in RUP: 15.10.2013; Views: 4261; Downloads: 50
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8. 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: 3757; Downloads: 230
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9. Zhao, L.; Hou, J.: Jordan zero-product preserving additive maps on operator algebras. (English). - [J] J. Math. Anal. Appl. 314, No. 2, 689-700 (2006). [ISSN 0022-247X]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, operatorske algebre, jordanski ničelni produkti, jordanski homomorfizmi
Published in RUP: 15.10.2013; Views: 3995; Downloads: 35
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10. Generalized bicircular projections via rank preserving maps on the spaces of symmetric and antisymmetric operatorsAjda Fošner, Dijana Ilišević, 2011, original scientific article Abstract: V članku so obravnavane naslednje, med seboj povezane, preslikave na simetričnih in antisimetričnih operatorjih, ki delujejo na kompleksnem Hilbertovem prostoru: linearni ohranjevalci ranga ena na simetričnih operatorjih, linearni ohranjevalci ranga dva na antisimetričnih operatorjih, surjektivne linearne izometrije in posplošeni bicirkularni projektorji.
Keywords: matematika, teorija operatorjev, posplošene bicirkularni projektorji, ohranjevalci ranga, simetrični operatorji, antisimetrični operatorji
Published in RUP: 15.10.2013; Views: 3076; Downloads: 78
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