Premium
One‐Parameter Groups Arising from Real Subspaces of Self‐Dual Hilbert W * ‐Moduli
Author(s) -
Frank Michael
Publication year - 1990
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19901450113
Subject(s) - mathematics , noncommutative geometry , linear subspace , moduli , pure mathematics , hilbert space , commutative property , unitary state , dual (grammatical number) , moduli space , interpretation (philosophy) , algebra over a field , quantum mechanics , art , physics , literature , political science , computer science , law , programming language
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.