The invariant subspaces of the shift plus integer multiple of Volterra operator on Hardy spaces

Abstract

Čučković and Paudyal recently characterized the lattice of invariant subspaces of the shift plus a complex Volterra operator on the Hilbert space $H^2$ 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 $H^p$, which essentially extends their works to the more general cases when $1\le p<\infty$.

arXiv comment8 pages, accepted for publication in Archiv der Mathematik