Nearly invariant subspaces in the real Hardy space

TL;DR

This paper investigates nearly invariant subspaces of the backward shift operator on the real Hardy space, providing characterizations for subspaces with finite defect and almost invariance.

Contribution

It offers a new characterization of almost invariant subspaces of the backward shift operator in the real Hardy space.

Findings

Characterization of nearly invariant subspaces with finite defect

Description of almost invariant subspaces of the backward shift

Advancement in understanding the structure of invariant subspaces

Abstract

The objective of this article is to study nearly invariant subspaces of the backward shift operator on the real Hardy space. We also investigate nearly invariant subspaces with finite defect, and as a consequence, provide a characterization for almost invariant subspaces of the backward shift operator.