From random sets to continuous tensor products: answers to three questions of W. Arveson

Abstract

The set of zeros of a Brownian motion gives rise to a product system in the sense of William Arveson (that is, a continuous tensor product system of Hilbert spaces). Replacing the Brownian motion with a Bessel process we get a continuum of non-isomorphic product systems.

arXiv comment13 pages, LaTeX2e

References in corpus (2)

• Unitary Brownian motions are linearizable
• Noise sensitivity on continuous products: an answer to an old question of J. Feldman

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• Three Ways to Representations of B^a(E)
• On Product Systems arising from Sum Systems
• An asymmetric multiparameter CCR flow
• The Index of (White) Noises and their Product Systems
• A Simple Proof of the Fundamental Theorem about Arveson Systems
• Representations of B^a(E)