Abstract
Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H and A(H) ⊆ B(H) be a standard operator algebra which is closed under the adjoint operation. Let F: A(H)→ B(H) be a linear mapping satisfying F(AA*A) = F(A)A*A + Ad(A*)A + AA*d(A) for all A ∈ A(H), where the associated linear mapping d: A(H) → B(H) satisfies the relation d(AA*A) = d(A)A*A + Ad(A*)A + AA*d(A) for all A ∈ A(H). Then F is of the form F(A) = SA − AT for all A ∈ A(H) and some S, T ∈ B(H), that is, F is a generalized derivation. We also prove some results concerning centralizers on A(H) and semisimple H*-algebras.
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Original Russian Text © S. Ali, A. Fošner, W. Jing, 2018, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2018, No. 1, pp. 3-12.
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Ali, S., Fošner, A. & Jing, W. On Generalized Derivations and Centralizers of Operator Algebras with Involution. J. Contemp. Mathemat. Anal. 53, 27–33 (2018). https://doi.org/10.3103/S1068362318010053
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DOI: https://doi.org/10.3103/S1068362318010053