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Free E0-Semigroups

Published online by Cambridge University Press:  20 November 2018

Neal J. Fowler
Neal J. Fowler*
Affiliation:
University of Calgary, Calgary, Alberta
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Abstract

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Given a strongly continuous semigroup of isometries ∪ acting on a Hilbert space ℋ, we construct an E0-semigroup α∪, the free E0-semigroup over ∪, acting on the algebra of all bounded linear operators on full Fock space over ℋ. We show how the semigroup αU⊗V can be regarded as the free product of α∪ and αV. In the case where U is pure of multiplicity n, the semigroup au, called the Free flow of rank n, is shown to be completely spatial with Arveson index +∞. We conclude that each of the free flows is cocycle conjugate to the CAR/CCR flow of rank +∞.

Keywords

46L4081E05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995 , pp. 744 - 785
Copyright
Copyright © Canadian Mathematical Society 1995

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