Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces

Abstract

We characterize the integration operators \(V_g\) with symbol g for which \(V_g\) acts as an absolutely summing operator on weighted Bloch spaces \(\mathcal {B}^{\beta }\) and on weighted Bergman spaces \(\mathscr {A}^p_\alpha \). We show that \(V_g\) is r-summing on \(\mathscr {A}^p_\alpha \), \(1 \le p <\infty \), if and only if g belongs to a suitable Besov space. We also show that there is no non trivial nuclear Volterra operators \(V_g\) on Bloch spaces and on Bergman spaces.