Premium
Von Neumann Representations on 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.19901450114
Subject(s) - mathematics , von neumann algebra , pure mathematics , bounded function , moduli , moduli space , von neumann architecture , affiliated operator , dual (grammatical number) , hilbert space , linear subspace , von neumann's theorem , commutative property , algebra over a field , mathematical analysis , physics , quantum mechanics , multiplication operator , art , literature
This paper continues the investigations of [4]. Von Neumann algebras M of bounded operators on self‐dual Hilbert W * ‐moduli ℋ possessing a cyclic‐separating element x in ℋ are considered. The close relation of them to such special real subspaces K of ℋ as treated in [4] is shown. Under the supposition that the underlying W * ‐algebra is commutative, a Tomita‐Takesaki type theorem is stated for von Neumann algebras on self‐dual Hilbert W * ‐moduli. The natural cone in ℋ arising from the pair ( M, x ) is investigated and its properties are obtained.