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

Povzetek

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 ▫$A \in A(X)$▫.

Ključne besede

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;

Podatki

Jezik:	Angleški jezik
Leto izida:	2012
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UM FNM - Fakulteta za naravoslovje in matematiko
UDK:	512.552
COBISS:	19200520
ISSN:	0017-095X
Št. ogledov:	398
Št. prenosov:	11
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 95-104
Letnik:	Vol. 47
Zvezek:	no. 1
Čas izdaje:	2012
ID:	1477045