Toeplitz CAR flows and type I factorizations

TL;DR

This paper studies Toeplitz CAR flows, a class of E_0-semigroups, demonstrating their diversity in type III examples and providing criteria to classify them as either type I or III, extending previous work by Powers and Arveson.

Contribution

It shows Toeplitz CAR flows include uncountably many non cocycle conjugate type III examples and generalizes the type III classification criterion.

Findings

Contains uncountably many non cocycle conjugate type III E_0-semigroups

Provides a criterion to classify Toeplitz CAR flows as type I or III

Extends the classification framework established by Powers and Arveson

Abstract

Toeplitz CAR flows are a class of E_0-semigroups including the first type III example constructed by R. T. Powers. We show that the Toeplitz CAR flows contain uncountably many mutually non cocycle conjugate E_0-semigroups of type III. We also generalize the type III criterion for Toeplitz CAR flows employed by Powers (and later refined by W. Arveson), and show that Toeplitz CAR flows are always either of type I or type III.