Bitraces on Partial O*-Algebras

Abstract

Unbounded bitraces on partial O*-algebras are considered, a class of ideals defined by them is exhibited, and several relationships between certain commutants, bicommutants, and tricommutants associated with the *-representations and *-antirepresentations determined by the bitraces are established. Moreover, a notion of a partial W*-algebra of unbounded densely defined linear maps on a Hilbert space, as a generalization of a W*-algebra, is introduced and a set of criteria for classifying such algebras by means of the type of bitraces that are defined on them is proposed.