On functional equations related to derivations in semiprime rings and standard operator algebras

Abstract

In this paper functional equations related to derivations on semiprime rings and standard operator algebras are investigated. We prove, for example, the following result, which is related to a classical result of Chernoff. Let ▫$X$▫ be a real or complex Banach space, let ▫$L(X)$▫ be the algebra of all bounded linear operators of ▫$X$▫ into itself and let ▫$A(X) \subset L(X)$▫ be a standard operator algebra. Suppose there exist linear mappings ▫$D,G \colon A(X) \to L(X)$▫ satisfying the relations ▫$D(A^3)=D(A^2)A + A^2G(A)$▫, ▫$G(A^3) = G(A^2)A + A^2D(A)$▫ for all ▫$A \in A(X)$▫. In this case there exists ▫$B \in L(X)$▫ such that ▫$D(A) = G(A) = [A,B]$▫ holds for all ▫$A \in A(X)$▫.

Keywords

matematika;algebra;prakolobar;polprakolobar;Banachov prostor;standardna operatorska algebra;odvajanje;jordansko odvajanje;jordansko trojno odvajanje;mathematics;prime ring;semiprime ring;Banach space;standard operator algebra;derivation;Jordan derivation;Jordan triple derivation;

Data

Language:	English
Year of publishing:	2012
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	19200520
ISSN:	0017-095X
Views:	398
Downloads:	11
Average score:	0 (0 votes)
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Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 95-104
Volume:	Vol. 47
Issue:	no. 1
Chronology:	2012
ID:	1477045