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On functional equations related to derivations in semiprime rings and standard operator algebrasŠirovnik, NejcIn 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 ▫$A \in A(X)$▫.Source: Glasnik matematički. Serija 3. - ISSN 0017-095X (Vol. 47, no. 1, 2012, str. 95-104)Type of material - article, component part ; adult, seriousPublish date - 2012Language - englishCOBISS.SI-ID - 19200520
Author
Širovnik, Nejc
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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Širovnik, Nejc | 33266 |
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