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Summary: PATH SPACES, CONTINUOUS TENSOR
PRODUCTS, AND E0-SEMIGROUPS
William Arveson
Department of Mathematics
University of California
Berkeley CA 94720, USA
Abstract. We classify all continuous tensor product systems of Hilbert spaces which
are "infinitely divisible" in the sense that they have an associated logarithmic struc-
ture. These results are applied to the theory of E0-semigroups to deduce that every
E0-semigroup possessing sufficiently many "decomposable" operators must be cocy-
cle conjugate to a CCR flow.
A path space is an abstraction of the set of paths in a topological space, on which
there is given an associative rule of concatenation. A metric path space is a pair
(P, g) consisting of a path space P and a function g : P2 C which behaves as if
it were the logarithm of a multiplicative inner product. The logarithmic structures
associated with infinitely divisible product systems are such objects. The preceding
results are based on a classification of metric path spaces.
Contents
Introduction
Part I. Path Spaces
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