Asymmetric truncated Toeplitz operators on finite-dimensional spaces II

TL;DR

This paper explores the structure and properties of asymmetric truncated Toeplitz operators in finite-dimensional spaces, providing characterizations and descriptions of rank-one operators, building on prior foundational work.

Contribution

It introduces new characterizations of these operators using modified compressed shifts and shift invariance, and describes rank-one cases in finite-dimensional model spaces.

Findings

Operators characterized via modified compressed shifts

Shift invariance used for operator description

Rank-one operators explicitly described

Abstract

In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be characterized using modified compressed shifts or the notion of shift invariance. We also describe rank-one asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. This paper is a sequel to the paper of J. Jurasik and B. {\L}anucha "Asymmetric truncated Toeplitz operators on finite-dimensional spaces".