Toeplitz CAR flows and type I factorizations

Masaki Izumi; R. Srinivasan

doi:10.1215/0023608X-2009-001

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Home > Journals > Kyoto J. Math. > Volume 50 > Issue 1 > Article

Spring 2010 Toeplitz CAR flows and type I factorizations

Masaki Izumi, R. Srinivasan

Kyoto J. Math. 50(1): 1-32 (Spring 2010). DOI: 10.1215/0023608X-2009-001

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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 canonical anticommutation relation (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.

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Masaki Izumi. R. Srinivasan. "Toeplitz CAR flows and type I factorizations." Kyoto J. Math. 50 (1) 1 - 32, Spring 2010. https://doi.org/10.1215/0023608X-2009-001