Generalized CCR Flows
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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.
KeywordsProduct System Toeplitz Operator Real Hilbert Space Spectral Density Function Complex Hilbert Space
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