Asymmetric truncated Toeplitz operators on finite-dimensional spaces

TL;DR

This paper studies asymmetric truncated Toeplitz operators between finite-dimensional model spaces, calculating their dimensions and describing their matrix representations, thus extending known results for symmetric cases.

Contribution

It generalizes the theory of truncated Toeplitz operators to asymmetric cases in finite-dimensional spaces, providing explicit dimension formulas and matrix descriptions.

Findings

Computed the dimension of the space of asymmetric truncated Toeplitz operators.

Described the matrix representations of these operators.

Extended known results from symmetric to asymmetric cases.

Abstract

In this paper we consider asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. We compute the dimension of the space of all such operators. We also describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces. Our results are generalizations of the results known for truncated Toeplitz operators.