Norms of truncated Toeplitz operators and numerical radii of restricted shifts

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.

arXiv comment26 pages. Final version, with some more corrections and clarifications