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Additive derivations of some operator algebras. (English) Zbl 0705.46035
Ill. J. Math. (to appear).
Summary: Let A be a standard operator algebra on an infinite dimensional Hilbert space X. We denote by \(B(X)\) the algebra of all bounded linear operators on X. It is proved that every additive derivation \(D: A\to B(X)\) is of the form \(D(A)=AT-TA\) for some \(T\in B(X).\)
A complete description of all additive derivations on \(B(X)\) in the case that X is finite dimensional is also given. In particular it is shown that in this case there exists an additive derivation \(D: B(X)\to B(X)\) which is not inner.
Reviewer: P.Šemrl

46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras