Jordan [tau]-derivations of locally matrix rings

Chuang, Chen-Lian; Fošner, Ajda; Lee, Tsiu Kwen

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Title:	Jordan [tau]-derivations of locally matrix rings
Authors:	ID Chuang, Chen-Lian (Author) ID Fošner, Ajda (Author) ID Lee, Tsiu Kwen (Author)
Files:	http://dx.doi.org/10.1007/s10468-011-9329-8
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
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
Year of publishing:	2013
Number of pages:	str. 755-763
Numbering:	Vol. 16, iss. 3
PID:	20.500.12556/RUP-2200
ISSN:	1386-923X
UDC:	512.552
COBISS.SI-ID:	16195673
Publication date in RUP:	15.10.2013
Views:	5655
Downloads:	86
Metadata:
:	CHUANG, Chen-Lian, FOŠNER, Ajda and LEE, Tsiu Kwen, 2013, Jordan [tau]-derivations of locally matrix rings. [online]. 2013. Vol. 16, no. 3, p. 755–763. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1007/s10468-011-9329-8 Copy citation

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Secondary language

Language:	Slovenian
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

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