On matrix valued (asymmetric) truncated Toeplitz operators

TL;DR

This paper introduces a new conjugation for matrix valued asymmetric truncated Toeplitz operators, explores their complex symmetry properties, and investigates their connections with Hankel operators with matrix symbols.

Contribution

It defines a novel conjugation and studies its relation to matrix valued asymmetric truncated Toeplitz operators, advancing understanding of their symmetry and connections to Hankel operators.

Findings

Matrix valued asymmetric truncated Toeplitz operators are generally not complex symmetric.

A new conjugation with unique properties is introduced.

Connections between these Toeplitz operators and Hankel operators with matrix symbols are established.

Abstract

Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators. We also explore the connections between matrix valued asymmetric truncated Toeplitz operators and Hankel operators with matrix symbols.