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

Abstract

A partial answer on [KS2, Question 2] is given. Namely, an operator $R$ similar to a quasianalytic contraction whose quasianalytic spectral set is equal to its spectrum and is a proper subarc of the unit circle is constructed, but no estimates of $\Vert R^{-1}\Vert$ is given.

References in corpus (3)

• Quasianalytic polynomially bounded operators
• Some sufficient conditions for existence of hyperinvariant subspaces for operators intertwined with unitaries
• Invertibility of functions of operators and existence of hyperinvariant subspaces