One-Parameter Groups Arising from Real Subspaces of Self-Dual Hilbert W*-Moduli

The purpose of this paper is to generalize the results of M. A. Rieffel and A. van Daele 8, §§ 1, 2, 3] for Hilbert W^*-moduli over commutative W^*-Algebras. Some special real subspaces of such Hilbert W^*-moduli and the related operators are investigated. Particularly, the relation is established between ^*weakly continuous unitary one-parameter groups of operators arising from them and the generalized K.M.S. condition. All key definitions are formulated without any commutativity supposition for the underlying W^*-algebra. The interpretation of these results is given for sets of continuous sections of “self-dual” locally trivial Hilbert bundles over hyperstonian compact spaces. At the end of this paper some aspects of the general noncommutative case are discussed.