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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 $B\left(X\right)$ the algebra of all bounded linear operators on X. It is proved that every additive derivation $D:A\to B\left(X\right)$ is of the form $D\left(A\right)=AT-TA$ for some $T\in B\left(X\right)·$

A complete description of all additive derivations on $B\left(X\right)$ 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 $D:B\left(X\right)\to B\left(X\right)$ which is not inner.

Reviewer: P.Šemrl
##### MSC:
 46L57 Derivations, dissipations and positive semigroups in ${C}^{*}$-algebras