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44. Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, izvirni znanstveni članek Opis: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫.
Ključne besede: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring
Objavljeno v RUP: 15.10.2013; Ogledov: 4123; Prenosov: 144
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48. Generalized bicircular projections via rank preserving maps on the spaces of symmetric and antisymmetric operatorsAjda Fošner, Dijana Ilišević, 2011, izvirni znanstveni članek Opis: 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.
Ključne besede: matematika, teorija operatorjev, posplošene bicirkularni projektorji, ohranjevalci ranga, simetrični operatorji, antisimetrični operatorji
Objavljeno v RUP: 15.10.2013; Ogledov: 3078; Prenosov: 78
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50. The Hyers-Ulam-Rassias stability of (m,n)[sub]{([sigma], [tau])}-derivations on normed algebrasAjda Fošner, 2012, izvirni znanstveni članek Opis: We study the Hyers-Ulam-Rassias stability of ▫$(m,n)_{(\sigma,\tau)}$▫-derivations on normed algebras.
Ključne besede: Hyers-Ulam-Rassias stability, normed algebra, ▫$(m,n)_{(\sigma,\tau)}$▫-derivation
Objavljeno v RUP: 15.10.2013; Ogledov: 3044; Prenosov: 35
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