1. Noninvertibility preservers on Banach algebrasBojan Kuzma, 2006, short scientific article Abstract: It is proved that a linear surjection ▫$\Phi: \mathcal{A} \to \mathcal{B}$▫, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective. Keywords: mathematics, functional analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle Published in RUP: 15.10.2013; Views: 3207; Downloads: 126 Link to full text |
2. Hyers-Ulam-Rassias stability of generalized module left (m,n)-derivationsAjda Fošner, 2013, original scientific article Abstract: The generalized Hyers-Ulam-Rassias stability of generalized module left ▫$(m,n)$▫-derivations on a normed algebra ▫$\mathcal{A}$▫ into a Banach left ▫$\mathcal{A}$▫-module is established. Keywords: Hyers-Ulam-Rassias stability, normed algebra, Banach left A-module, module left (m, n)-derivation, generalized module left (m, n)-derivation Published in RUP: 15.10.2013; Views: 3469; Downloads: 107 Link to full text |
3. On the generalized Hyers-Ulam stability of module left (m, n)-derivationsAjda Fošner, 2012, original scientific article Abstract: We study the generalized Hyers-Ulam stability of functional equations of module left ▫$(m, n)$▫-derivations. Keywords: mathematics, algebra, generalized Hyers-Ulam stability, normed algebra, Banach left A-module, module left ▫$(m, n)$▫-derivation Published in RUP: 15.10.2013; Views: 3551; Downloads: 131 Link to full text |
4. Jordan [tau]-derivations of locally matrix ringsChen-Lian Chuang, Ajda Fošner, Tsiu Kwen Lee, 2013, original scientific article Abstract: Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2 and let ▫$Q_{ms}(R)$▫ be the maximal symmetric ring of quotients of ▫$R$▫. Suppose that ▫$\delta \colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫-derivation, where ▫$\tau$▫ is an anti-automorphism of $R$. Then there exists ▫$a \in Q_{ms}(R)$▫ such that ▫$\delta(x) = xa - a\tau(x)$▫ for all ▫$x \in R$▫. Let ▫$X$▫ be a Banach space over the field ▫$\mathbb{F}$▫ of real or complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫. We prove that ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫, which provides the viewpoint of ring theory for some results concerning derivations on the algebra ▫$\mathcal{B}(X)$▫. In particular, all Jordan ▫$\tau$▫-derivations of ▫$\mathcal{B}(X)$▫ are inner if ▫$\dim_{\mathbb{F}} X>1$▫. Keywords: mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach space Published in RUP: 15.10.2013; Views: 3831; Downloads: 83 Link to full text |