Infinite Dimensional Ito Algebras of Quantum White Noise

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dc.creatorBelavkin, V. P.
dc.date2005-12-13
dc.date.accessioned2026-07-07T06:55:10Z
dc.date.available2026-07-07T06:55:10Z
dc.descriptionA simple axiomatic characterization of the general (infinite dimensional, noncommutative) Ito algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. The notion of Ito B*-algebra, generalizing the C*-algebra is defined to include the Banach infinite dimensional Ito algebras of quantum Brownian and quantum Levy motion, and the B*-algebras of vacuum and thermal quantum noise are characterized. It is proved that every Ito algebra is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Levy (Poisson) algebra. In particular, every quantum thermal noise is the orthogonal sum of a quantum Wiener noise and a quantum Poisson noise as it is stated by the Levy-Khinchin theorem in the classical case.
dc.description15 pages, read at the International Conference on Infinite Dimensional Analysis and Quantum Probability, Kyoto, 2000
dc.identifierhttps://arxiv.org/abs/math/0512288
dc.identifierhttp://arxiv.org/abs/math/0512288
dc.identifierTrends in Contemporary Infinite Dimensional Analysis and Quantum Probability 57--80, Instituto Italiano di Cultura, Kyoto, 2000
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106197
dc.subjectProbability
dc.subjectOperator Algebras
dc.titleInfinite Dimensional Ito Algebras of Quantum White Noise
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