Norms of truncated Toeplitz operators and numerical radii of restricted shifts

TL;DR

This paper introduces a novel method for calculating the numerical radius of restricted shift operators by relating it to the norm of truncated Toeplitz operators, providing new insights and resolving a conjecture on compact TTO symbols.

Contribution

It establishes a new approach linking numerical radius to TTO norms and resolves a conjecture on continuous symbols for compact TTOs.

Findings

Linked numerical radius of restricted shifts to TTO norms

Derived new results on TTO norms

Resolved a conjecture on continuous symbols for compact TTOs

Abstract

This paper gives a new approach to the calculation of the numerical radius of a restricted shift operator by linking it to the norm of a truncated Toeplitz operator (TTO), which can be be calculated by various methods. Further results on the norm of a TTO are derived, and a conjecture on the existence of continuous symbols for compact TTO is resolved.