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Some remarks on derivations in semiprime rings and standard operator algebrasVukman, JosoIdentities 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.Source: Glasnik matematički. Serija 3. - ISSN 0017-095X (Vol. 46, no. 1, 2011, str. 43-48)Type of material - article, component part ; adult, seriousPublish date - 2011Language - englishCOBISS.SI-ID - 18432264
Author
Vukman, Joso
Topics
matematika |
algebra |
prakolobar |
polprakolobar |
Banachov prostor |
standardna operatorska algebra |
odvajanje |
jordansko odvajanje |
jordansko trojno odvajanje |
mathematics |
algebra |
prime ring |
semiprime ring |
Banach space |
standard operator algebra |
derivation |
Jordan derivation |
Jordan triple derivation
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