Hilbert modules are an invaluable tool in the study of dynamical systems both classical and quantum. Starting from the description of the universal Markov process of a semigroup of transition kernels in terms of Hilbert modules, motivating in this way carefully also how the notion emerges naturally, we illustrate some of the consequences. Several of these consequences relate a Markov process (that is, a classical irreversible dynamical system) to questions about irreversible and reversible quantum dynamical systems.

Hilbert Modules in Probability

Michael Skeide
2019-01-01

Abstract

Hilbert modules are an invaluable tool in the study of dynamical systems both classical and quantum. Starting from the description of the universal Markov process of a semigroup of transition kernels in terms of Hilbert modules, motivating in this way carefully also how the notion emerges naturally, we illustrate some of the consequences. Several of these consequences relate a Markov process (that is, a classical irreversible dynamical system) to questions about irreversible and reversible quantum dynamical systems.
2019
979-12-200-4788-3
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11695/91591
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