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arXiv · 2410.14893

Product systems arising from L\'evy processe

Remus Floricel·Peter Wadel
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Abstract

This paper investigates the structure of product systems of Hilbert spaces derived from Banach space-valued L\'evy processes. We establish conditions under which these product systems are completely spatial and show that Gaussian L\'evy processes with non-degenerate covariance always give rise to product systems of type I. Furthermore, we construct a continuum of non-isomorphic product systems of type \(\rm{II}\sb\infty\) from pure jump L\'evy processes.

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Remus Floricel, Peter Wadel. 2024-10-18. Product systems arising from L\'evy processe. https://doi.org/10.1016/j.jfa.2025.111087

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