Non-commutative chaotic expansion of Hilbert-Schmidt operators on Fock space |
| |
Authors: | Stéphane Attal |
| |
Institution: | (1) Institut de Recherche Mathématique Avancée, Université Louis Pasteur et C.N.R.S., 7, rue René Descartes, F-67084 Strasbourg Cedex, France |
| |
Abstract: | It is known, from a simple algebraic computation, that every Hilbert-Schmidt operator on the Fock space admits a Maassen-Meyer kernel. Maassen-Meyer kernels are a non-commutative extension of the usual notion of chaotic expansion of random variables. Using an extension of the non-commutative stochastic integrals which allows to define these integrals on the whole Fock space, we prove that a Hilbert-Schmidt operator on Fock space is the sum of a series of iterated non-commutative stochastic integrals with respect to the basic theree quantum noises. In this way we recover its Maassen-Meyer kernel which can be completely described from the operator itself. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|