Invariant subspaces of the shift plus complex Volterra operator

The lattice of closed invariant subspaces of the Volterra operator acting on L2(0,1)L2(0,1) was completely described by Sarason [8]. On the other hand, he explicitly found the lattice of closed invariant subspaces of the shift plus Volterra operator on L2(0,1)L2(0,1) in [9]. Inspired by Sarason's results, we find the lattice of closed invariant subspaces of the shift plus complex Volterra operator acting on the Hardy space.