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

Volume 263 / 2022

Maria F. Gamal’ 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.

Authors

  • Maria F. Gamal’St. Petersburg Branch
    V. A. Steklov Institute of Mathematics
    Russian Academy of Sciences
    Fontanka 27
    St. Petersburg, 191023, Russia
    e-mail

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