Rank one perturbations of 2-isometries

TL;DR

This paper studies conditions under which rank-one perturbations of 2-isometries preserve their 2-isometry property and explores classes of such operators on function spaces.

Contribution

It characterizes when rank-one perturbations of 2-isometries remain 2-isometries and identifies specific classes of these operators on function spaces.

Findings

Conditions for rank-one perturbations to preserve 2-isometry

Identification of classes of 2-isometries on function spaces

Insights into the structure of 2-isometries under perturbations

Abstract

In this paper, we investigate when a rank-one perturbation of a $2$-isometry remains a $2$-isometry. As an application, we identify several classes of $2$-isometries on function spaces.