Almost invariant subspaces of the shift operators on vector-valued spaces

Release time:2026-03-20

Journal:Submitted

Abstract:In this paper we characterize almost invariant subspaces of the shift operators on vector-valued space. Firstly, we establish the Beurling-Lax-Halmos Theorem for almost invariant subspaces, that is, a characterization of almost invariant subspaces of the backward shift $S_E^*$ on the vector-valued Hardy space $H^2_E$. Secondly, we establish a complete characterization for almost invariant subspaces of the bilateral shift $B_E$ on the vector-valued $L^{2}$ space whose scalar-valued version largely answers the question posed by Chalendar-Gallardo-Partington in 2020.

Co-author:Caixing Gu, In Sung Hwang, Woo Young Lee, Pan Ma

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Translation or Not:no