Hyperinvariant subspaces for normaloid essential isometric operators

TL;DR

This paper establishes the existence of non-trivial hyperinvariant subspaces for certain classes of perturbed partial isometries, including those with Schatten class perturbations, expanding understanding of operator invariant subspace theory.

Contribution

It proves the existence of hyperinvariant subspaces for a new class of compact perturbations of scalar multiples of partial isometries, including Schatten class perturbations.

Findings

Existence of hyperinvariant subspaces for specific operator classes

Inclusion of important classes of operators within the studied subclass

Extension to Schatten class perturbations with finite-dimensional null space

Abstract

In this article, we prove the existence of a non-trivial hyperinvariant subspace for a subclass of compact perturbations of scalar multiple of a partial isometry. Later, we illustrate that this class contains several important classes of operators. As a consequence, we prove that a Schatten class perturbation of a partial isometry with finite-dimensional null space has a non-trivial hyperinvariant subspace.