The Norm of a Truncated Toeplitz Operator

TL;DR

This paper establishes lower bounds for the norm of truncated Toeplitz operators and explores the relationship between $H^2$ and $H^{ }infty$ norms within model spaces, advancing understanding of their operator norms.

Contribution

It provides new lower bounds for truncated Toeplitz operator norms and reveals a novel relationship between $H^2$ and $H^{ }infty$ norms in model spaces.

Findings

Derived several lower bounds for the norm of truncated Toeplitz operators.

Discovered a curious relationship between $H^2$ and $H^{ }infty$ norms in model spaces.

Abstract

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the $H^2$ and $H^{\infty}$ norms of functions in model spaces.