Riesz Transforms on Deformed Fock Spaces

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. Received: 24 November 1998 / Accepted: 2 March 1999