Volterra type operators on minimal Mobius invariant space

Abstract

In this note, we mainly study operator-theoretic properties on Besov space B 1 on the unit disc. This space is the minimal Möbius invariant space. Firstly, we consider the boundedness of Volterra type operators. Secondly, we prove that Volterra type operators belong to the Deddens algebra of composition operator. Thirdly, we obtain estimates for the essential norm of Volterra type operators. Finally, we give a complete characterization of spectrum of Volterra type operators. D(1 − |z| 2 ) p−2 |f ′ (z)| p dA(z) < ∞.