# Matrix valued truncated Toeplitz operators: basic properties

## TL;DR

This paper investigates matrix valued truncated Toeplitz operators acting on vector-valued model spaces, generalizing block Toeplitz matrices, and provides characterizations and symbol descriptions for these operators.

## Contribution

It offers a characterization of matrix valued truncated Toeplitz operators and identifies symbols that produce the zero operator, extending scalar results to the matrix case.

## Key findings

- Characterization of matrix valued truncated Toeplitz operators
- Identification of symbols producing the zero operator
- Extension of scalar case results to matrix-valued operators

## Abstract

Matrix valued truncated Toeplitz operators act on vector-valued model spaces. They represent a generalization of block Toeplitz matrices. A characterization of these operators analogue to the scalar case is obtained, as well as the determination of the symbols that produce the zero operator.