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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:AB(X) is of the form D(A)=AT-TA for some TB(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)B(X) which is not inner.

Reviewer: P.Šemrl
MSC:
46L57Derivations, dissipations and positive semigroups in C * -algebras