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The invariant subspaces of the shift plus integer multiple of Volterra operator on Hardy spaces (1803.06623v2)
Published 18 Mar 2018 in math.CV
Abstract: \v{C}u\v{c}kovi\'{c} and Paudyal recently characterized the lattice of invariant subspaces of the shift plus a complex Volterra operator on the Hilbert space $H2$ on the unit disk. Motivated by the idea of Ong, in this paper, we give a complete characterization of the lattice of invariant subspaces of the shift operator plus a positive integer multiple of the Volterra operator on Hardy spaces $Hp$, which essentially extends their works to the more general cases when $1\leq p<\infty$.