Local Derivations, Automorphisms and Commutativity Preserving Maps on $\mathscr L^+(\mathscr D)$

In this paper we study linear operators 0: J&?~u(^) > J*f + (^), where 2 is a dense linear subspace in a Hilbert-space Jf. jf + (S) is a *-algebra which in general contains unbounded operators. Such *-algebras of unbounded operators have been studied for more than 20 years (see e. g. Much results of this theory state analogies between *-algebras of unbounded operators and algebras of bounded operators. That will be the case also in this paper. We want to generalize results of LARSON, SOUROUR and OMLADIC (see

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