Volterra operators between limits of Bergman-type weighted spaces of analytic functions

Abstract

We characterize continuity and compactness of the Volterra integral operator $T_g$ with the non-constant analytic symbol $g$ between certain weighted Fréchet or (LB)-spaces of analytic functions on the open unit disc, which arise as projective (resp. inductive) limits of intersections (resp. unions) of Bergman spaces of order $1<p<\infty$ induced by the standard radial weight $(1-|z|^2)^\alpha$ for $0<\alpha<\infty$. Motivated from the earlier results obtained for weighted Bergman spaces of standard weight, we also establish several results concerning the spectrum of the Volterra operators acting on the weighted Bergman Fréchet space $A^p_{\alpha+}$, and acting on the weighted Bergman (LB)-space $A^p_{\alpha-}$.