Chen-Lian Chuang (Author), Ajda Fošner (Author), Tsiu Kwen Lee (Author)

Abstract

Naj bo ▫$R$▫ lokalno matrični prakolobar s karakteristiko različno od 2 in ▫$Q_{ms}(R)$▫ maksimalni simetrični kolobar kvocientov kolobarja ▫$R$▫. Naj bo ▫$\delta \colon R \to Q_{ms}(R)$▫ jordansko ▫$\tau$▫-odvajanje, kjer je ▫$\tau$▫ antiavtomorfizem kolobarja ▫$R$▫. Potem obstaja tak ▫$a \in Q_{ms}(R)$▫, da je ▫$\delta(x) = xa - a\tau(x)$▫ za vse ▫$x \in R$▫. Naj bo ▫$X$▫ Banachov prostor nad kompleksnim ali realnim poljem ▫$\mathbb{F}$▫ in ▫$\mathcal{B}(X)$▫ algebra omejenih linearnih operatorjev na ▫$X$▫. V članku je dokazano, da je ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫.

Keywords

matematika;algebra;antiavtomorfizem;lokalno matrični kolobar;prakolobar;jordanski homomorfizem;jordansko ▫$\tau$▫-odvajanje;Banachov prostor;mathematics;anti-automorphism;locally matrix ring;prime ring;Jordan homomorphism;Jordan ▫$\tau$▫-derivation;Banach space;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UP - University of Primorska
UDC: 512.552
COBISS: 16195673 Link will open in a new window
ISSN: 1386-923X
Views: 3544
Downloads: 83
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Other data

Secondary language: Slovenian
Secondary title: Jordanska [tau]-odvajanja na lokalno matričnih kolobarjih
Secondary 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 ▫$\dim_{\mathbb{F}} X>1$▫.
Secondary keywords: matematika;algebra;antiavtomorfizem;lokalno matrični kolobar;prakolobar;jordanski homomorfizem;jordansko ▫$\tau$▫-odvajanje;Banachov prostor;
Type (COBISS): Not categorized
Pages: str. 755-763
Volume: ǂVol. ǂ16
Issue: ǂiss. ǂ3
Chronology: 2013
ID: 1476336