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On generalized derivations in Banach algebras

Nadia BoudiSaid Ouchrif — 2009

Studia Mathematica

We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.

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