Riesz Transforms on Deformed Fock Spaces

Abstract

The Fock Von Neumann algebra \(\), equipped with its canonical trace τ, is spanned by n hermitian operators \(\) acting on a Hilbert Fock space \(\) some commutation relations between \(\) and \(\) are defined by the n×n hermitian matrix A. We define a Riesz transform \(\), where \(\) is the number operator, ∇′ is aninner derivation (unbounded in general) and \(\). Let 1<p<∞. We prove that \(\) is equivalent to \(\) for every \(\) with null trace, with constants which do not depend on n.