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identities Bresar, M. and Vukman, J., Jordan derivations on prime rings, Bull. Austra Math. Soc. , 37 (1988), 321-322. MR 89f:16049 Jordan derivations on

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Brešar, M. and Vukman, J. , Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321–322. MR 89f :16049 Vukman J. Jordan derivations on prime rings

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. [2] Brešar , M. 2005 Jordan derivations revisited Math. Proc. Camb. Phil. Soc. 139 411 – 425 10.1017/S0305004105008601

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Summary  

Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on  X, and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D: A(X) → L(X) satisfying the relation D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all AA(X) and some B L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras.

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Summary  

Let Abe a semisimple H*-algebra and let T: AAbe an additive mapping such that T(x n +1)=T(x)x n+x n T(x) holds for all xAand some integer n≥1. In this case Tis a left and a right centralizer.

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Abstract  

The main purpose of this paper is to prove the following result. Let H be a complex Hilbert space, let
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{B}$$ \end{document}
(H) be the algebra of all bounded linear operators on H, and let
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(H) ⊂
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(H) be a standard operator algebra which is closed under the adjoint operation. Suppose that T:
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(H) →
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(H) is a linear mapping satisfying T(AA* A) = T(A)A* AAT(A*)A + AA*T(A) for all A
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{A}$$ \end{document}
(H). Then T is of the form T(A) = AB + BA for all A
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(H), where B is a fixed operator from
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(H). A result concerning functional equations related to bicircular projections is proved
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Molnár, L., Jordan *-derivation pairs on a complex *-algebra, Aequationes Math. 54 (1997), 44-55. MR 98j :46053 Jordan *-derivation pairs on a complex *-algebra

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. Hungar. 69 301 325 Zalar, B., Jordan *-derivation pairs and quadratic functionals on modules over *-rings

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