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1.
On generalized Jordan triple ([alpha], [beta]) [sup] [ast]-derivations and related mappings
Shakir Ali, Ajda Fošner, Maja Fošner, Mohammad Salahuddin Khan, 2013, izvirni znanstveni članek

Opis: Let ▫$R$▫ be a 2-torsion free semiprime ▫$\ast$▫-ring and let ▫$\alpha, \beta$▫ be surjective endomorphisms of ▫$R$▫. The aim of the paper is to show that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on ▫$R$▫ is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. This result makes it possible to prove that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on a semisimple ▫$H^\ast$▫-algebra is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. Finally, we prove that every Jordan triple left ▫$\alpha^\ast$▫-centralizer on a 2-torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫-centralizer.
Najdeno v: ključnih besedah
Ključne besede: mathematics, algebra, semiprime ▫$\ast$▫-ring, ▫$H^\ast$▫-algebra, Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, Jordan triple left ▫$\alpha^\ast$▫-centralizer
Objavljeno: 15.10.2013; Ogledov: 1479; Prenosov: 24
URL Polno besedilo (0,00 KB)

2.
Jordan [tau]-derivations of locally matrix rings
Chen-Lian Chuang, Ajda Fošner, Tsiu Kwen Lee, 2013, izvirni znanstveni članek

Opis: 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 ▫$\dim_{\mathbb{F}} X>1$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...\colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫-derivation, where ▫$\tau$▫ is an anti-automorphism of $R$....
Ključne besede: mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach space
Objavljeno: 15.10.2013; Ogledov: 1478; Prenosov: 21
URL Polno besedilo (0,00 KB)

3.
Jordan triple product homomorphisms
Bojan Kuzma, 2006, izvirni znanstveni članek

Opis: Nondegenerate mappings that preserve Jordan triple product on ▫${\mathscr{M}}_n({\mathbb{F}}$▫ are characterized. Here, ▫$n \ge 3$▫ and ▫$\mathbb{F}$▫ is an arbitrary field.
Najdeno v: ključnih besedah
Ključne besede: mathematics, linear algebra, matrix algebra, Jordan triple product, nonlinear preserver
Objavljeno: 15.10.2013; Ogledov: 1634; Prenosov: 66
URL Polno besedilo (0,00 KB)

4.
A note on generalized (m,n)-Jordan centralizers
Ajda Fošner, 2013, izvirni znanstveni članek

Opis: The aim of this paper is to define generalized ▫$(m, n)$▫-Jordan centralizers and to prove that on a prime ring with nonzero center and ▫${\rm char}(R) \ne 6mn(m+n)(m+2n)$▫ every generalized ▫$(m, n)$▫-Jordan centralizer is a two-sided centralizer.
Najdeno v: ključnih besedah
Ključne besede: mathematics, prime ring, semiprime ring, left (right) centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer, generalized (m, n)-Jordan centralizer
Objavljeno: 15.10.2013; Ogledov: 1361; Prenosov: 58
URL Polno besedilo (0,00 KB)
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5.
Mappings that preserve pairs of operators with zero triple Jordan product
Gorazd Lešnjak, Tatjana Petek, Chi-Kwong Li, Bojan Kuzma, Mirko Dobovišek, 2007, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Ključne besede: matrix algebra, Jordan triple product, nonlinear preservers
Objavljeno: 03.04.2017; Ogledov: 757; Prenosov: 49
URL Polno besedilo (0,00 KB)

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