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Generalized derivable mappings at zero point on some reflexive operator algebras

✍ Scribed by Jun Zhu; Changping Xiong

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 237 KB
Volume: 397
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.11.012

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✦ Synopsis

Let A be a subalgebra with the unit operator I in B(H ), we say that a linear mapping ϕ from A into B(H ) is a generalized derivable mapping at zero point if ϕ(ST ) = ϕ(S)T + Sϕ(T ) -Sϕ(I )T for any S, T ∈ A with ST = 0. In this paper, we show the following main result: every norm-continuous generalized derivable mapping at zero point on finite CSL algebras is a generalized derivation.

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