Some remarks on derivations in semiprime rings and standard operator algebras

Abstract

Identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes 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 ▫$A(X) \subseteq L(X)$▫ be a standard operator algebra. Suppose there exists a linear mapping ▫$D:A(X) \to L(X)$▫ satisfying the relation ▫$2D(A^{3}) = D(A^2)A + A^2D(A) + D(A)A^2 + AD(A^2)$▫ for all ▫$A \in A(X)$▫. In this case ▫$D$▫ is of the form ▫$D(A) = AB-BA$▫ for all ▫$A \in A(X)$▫ and some fixed ▫$B \in L(X)$▫, which means that ▫$D$▫ is a linear derivation.

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:	2011
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	18432264
ISSN:	0017-095X
Views:	385
Downloads:	37
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 43-48
Volume:	Vol. 46
Issue:	no. 1
Chronology:	2011
ID:	1477037