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Communications in Mathematical Physics

, Volume 281, Issue 2, pp 529–571 | Cite as

Generalized CCR Flows

  • Masaki Izumi
  • R. Srinivasan
Article

Abstract

We introduce a new construction of E 0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C 0-semigroups. We get a new necessary and sufficient condition for them to be of type III, when the associated sum system is of finite index. Using this criterion, we construct examples of type III E 0-semigroups, which can not be distinguished from E 0-semigroups of type I by the invariants introduced by Boris Tsirelson. Finally, by considering the local von Neumann algebras, and by associating a type III factor to a given type III E 0-semigroup, we show that there exist uncountably many type III E 0-semigroups in this family, which are mutually non-cocycle conjugate.

Keywords

Product System Toeplitz Operator Real Hilbert Space Spectral Density Function Complex Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceKyoto UniversityKyotoJapan
  2. 2.Chennai Mathematical InstituteSiruseriIndia

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