Function Theory on Cartan Domains and the Berezin-Toeplitz Symbol Calculus

Abstract

Cn with dv(z) normalized Lebesgue measure on 9. We let L = L2(Q, dv) be the usual space of Lebesgue square-integrable complex-valued functions on 9. By H2 = H2(Q, dv) we denote the Bergman subspace of L2 consisting of holomorphic functions. The orthogonal projection operator from L2 onto H2 is denoted by P. Forf in L-(Q), the space of essentially bounded, measurable functions on 9, we will consider the multiplication operator