## Example of a quasianalytic contraction whose spectrum is a proper subarc of the unit circle

### Volume 263 / 2022

Studia Mathematica 263 (2022), 89-120
MSC: Primary 47B02, 47A10, 47A15; Secondary 47A60.
DOI: 10.4064/sm201220-17-6
Published online: 13 September 2021

#### Abstract

A partial answer to a question of Kérchy and Szalai (2015) is given. Namely, it is proved that there exists a quasianalytic contraction whose quasianalytic spectral set is equal to its spectrum and is a proper subarc of the unit circle, but no estimates of the norm of its inverse are given.