Path spaces, continuous tensor products, and E_0 semigroups

Details Path spaces, continuous tensor products, and E_0 semigroups Path spaces, continuous tensor products, and E_0 semigroups

1994-11-20

arxiv.org/abs/funct-an/9411006v2

Mathematics

Operator Algebras

80 pages, AMSTeX 2.0, Please Note..this is the full version of a previously-posted file that was somehow truncated in transit

Scientific paper

We classify all continuous tensor product systems of Hilbert spaces which are ``infinitely divisible" in the sense that they have an associated logarithmic structure. These results are applied to the theory of E_0 semigroups to deduce that every E_0 semigroup which possesses sufficiently many ``decomposable" operators must be cocycle 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:P^2 --> complex numbers 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.

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