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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

##### MSC:
 46L57 Derivations, dissipations and positive semigroups in $$C^*$$-algebras