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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

46L57Derivations, dissipations and positive semigroups in $C^*$-algebras