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  • On derivations of algebras with involution
    Vukman, Joso
    Let ▫$X$▫ be a complex Hilbert space, let ▫$L(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫, and let ▫$A(X)\subset L(X)$▫ be a standard operator algebra, which is closed under the ... adjoint operation. Suppose there exists a linear mapping ▫$D : A(X) \to L(X)$▫ satisfying the relation ▫$D(AA^{\ast}A)=D(A)A^{\ast}A+AD(A^{\ast}D(A)$▫, 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 ▫$B \in L(X)$▫, which means that ▫$D$▫ is a derivation. We apply this result to semisimple ▫$H^{\ast}$▫-algebras.
    Vir: Acta mathematica Hungarica. - ISSN 0236-5294 (Vol. 112, no. 1/2, 2006, str. 187-192)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2006
    Jezik - angleški
    COBISS.SI-ID - 14635528

vir: Acta mathematica Hungarica. - ISSN 0236-5294 (Vol. 112, no. 1/2, 2006, str. 187-192)

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