Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On matrix valued (asymmetric) truncated Toeplitz operators

Nihat Gokhan Gogus, Rewayat Khan

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.

On matrix valued (asymmetric) truncated Toeplitz operators

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.
Paper Structure (5 sections, 10 theorems, 75 equations)

This paper contains 5 sections, 10 theorems, 75 equations.

Table of Contents

  1. Introduction
  2. Vector valued function spaces and their operators
  3. Model spaces and their decompositions
  4. Conjugations on model spaces
  5. Connection with matrix valued Hankel operators

Key Result

Proposition 3.1

Let $\Theta, \Lambda$, and $\Psi$ be $\Gamma$-symmetric inner functions such that $\Theta=\Lambda\Psi$. Then, $\Lambda$ and $\Psi$ commute.

Theorems & Definitions (19)

  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • Theorem 4.1
  • proof
  • Theorem 4.2
  • proof
  • Proposition 4.3
  • proof
  • ...and 9 more