Abstract. Let M be a von Neumann algebra and 5 and T be commuting "-automorphisms on M satisfying the equation: 5 + S"1 = T + T~l. It is proved that M can be decomposed by a central projection p in M such that S = T on Mp and S= T-1 on M(\ -p).

No abstract

No abstract

Abstract. In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.

Stochastic generalizations of some fixed point theorems on a class of nonconvex sets in a locally bounded topological vector space are established. As applications, Brosowski-Meinardus type theorems about random invariant approximation are obtained. This work extends or provides stochastic versions of several well known results.