Quantum Ito B*-algebras, their Classification and Decomposition

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dc.creatorBelavkin, V. P.
dc.date2005-12-21
dc.date.accessioned2026-07-07T06:55:38Z
dc.date.available2026-07-07T06:55:38Z
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.description12 pages. See relevant papers at http://www.maths.nott.ac.uk/personal/vpb/research/cha_noi.html http://www.maths.nott.ac.uk/personal/vpb/research/ana_cal.html
dc.identifierhttps://arxiv.org/abs/math/0512508
dc.identifierhttp://arxiv.org/abs/math/0512508
dc.identifierQuantum Probability 43 63--70 Banach Center Publications, Warszawa 1998
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106347
dc.subjectOperator Algebras
dc.subjectQuantum Algebra
dc.titleQuantum Ito B*-algebras, their Classification and Decomposition
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