On Generalized Derivations and Centralizers of Operator Algebras with Involution |
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| Authors: | Email author" target="_blank">S?AliEmail author A?Fo?ner W?Jing |
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| Institution: | 1.King Abdulaziz University,Jeddah,Saudi Arabia;2.Aligarh Muslim University,Aligarh,India;3.University of Primorska,Koper,Slovenia;4.Fayetteville State University,Fayetteville,USA |
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| 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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