On Quantum Itô Algebras and Their Decompositions
نویسنده
چکیده
A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular, every quantum thermal noise of a nite number of degrees of freedom is the orthogonal sum of a quantum Wiener noise and a quantum Poisson noise as it is stated by the Lévy-Khinchin theorem in the classical case. Two basic examples of non-commutative Itô nite group algebras are considered.
منابع مشابه
Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
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