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arxiv: math/0001070 · v1 · submitted 2000-01-12 · 🧮 math.FA · math.PR

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

Boris Tsirelson This is my paper
classification 🧮 math.FA math.PR
keywords productarvesonbrowniancontinuousmotionsystemtensoranswers
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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.

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    Establishes conditions for complete spatiality of product systems from Lévy processes and constructs a continuum of non-isomorphic type II_∞ systems from pure jump Lévy processes.