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.
From random sets to continuous tensor products: answers to three questions of W. Arveson
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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.
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2024 1verdicts
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Product systems arising from L\'evy processe
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.