Some remarks on derivations in semiprime rings and standard operator algebras

Povzetek

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.

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:	2011
Tipologija:	1.01 - Izvirni znanstveni članek
Organizacija:	UM FNM - Fakulteta za naravoslovje in matematiko
UDK:	512.552
COBISS:	18432264
ISSN:	0017-095X
Št. ogledov:	385
Št. prenosov:	37
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
URN:	URN:SI:UM:
Vrsta dela (COBISS):	Delo ni kategorizirano
Strani:	str. 43-48
Letnik:	Vol. 46
Zvezek:	no. 1
Čas izdaje:	2011
ID:	1477037