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Summary: INFINITE TENSOR PRODUCTS OF
COMPLETELY POSITIVE SEMIGROUPS
William Arveson
and
Geoffrey Price
Department of Mathematics
University of California
Berkeley CA 94720, USA
Department of Mathematics
U. S. Naval Academy
Annapolis, MD 21402, USA
Abstract. We construct a new class of semigroups of completely positive maps
on B(H) which can be decomposed into an infinite tensor product of such semi-
groups. Under suitable hypotheses, the minimal dilations of these semigroups to
E0-semigroups are pure, and have no normal invariant states. Concrete examples
are discussed in some detail.
Dedicated to Robert T. Powers on the occasion of his sixtieth birthday
1. Introduction.
An E0-semigroup is a semigroup of normal unital -endomorphisms = {t :
t 0} acting on the algebra B(H) of all bounded operators on a separable Hilbert
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