Standard generalized vectors for partial O*-algebras
(1997) Institut Henri Poincare. Annales: Physique Theorique — Vol. 67, n° 3, p. 223-258 (1997)
Files
No attached file found for this publication.
Details
- Authors
Antoine, Jean-Pierre 
- Abstract
- Standard generalized vectors for an O*-algebra N lead to a Tomita-Takesaki theory of modular automorphisms on N, and this is a key step in constructing KMS states on N (which would represent equilibrium states if N is the observable algebra of some physical system). In this paper, we extend to partial O*-algebras the notion of standard generalized vector and we show that they indeed satisfy the KMS condition. We also discuss several less restrictive classes of generalized vectors for a partial O*-algebra M, which all give rise to standard generalized vectors for a partial GW*-algebra canonically associated to M, either on the same domain or on a smaller dense domain. Finally we discuss the extension of standard generalized vectors from a von Neumann algebra U to a suitable partial GW*-algebra containing U. Thus here also partial GW*-algebras play a distinguished role among all partial O*-algebras.
- Affiliations
Citations
Antoine, J.-P., Inoue, A., & Ogi, H. (1997). Standard generalized vectors for partial O*-algebras. Institut Henri Poincare. Annales: Physique Theorique, 67(3), 223-258. https://hdl.handle.net/2078.5/28332 (Original work published 1997)