Trace ideal criteria for Toeplitz operators

AbstractFor a complex measure μ on the open unit disk U define an operator Tμ on a Hilbert space H of analytic functions with reproducing kernel k(z, w) by u. For a certain scale of Hilbert spaces Hα, α < 1, which includes the Hardy space H2 and weighted Bergman spaces A2, β, conditions are obtained which imply Tμ belongs to a Schatten ideal Sp. If μ is a positive measure then these conditions are necessary and sufficient. Application to composition operators and restriction operators are indicated