  In this note, we mainly study operator-theoretic properties on Besov space
$B_{1}$ on the unit disc. This space is the minimal Mobius 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.
