Some sufficient conditions for the existence of hyperinvariant subspaces for operators intertwined with unitaries

Gamal, Maria F.

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: STUDIA MATHEMATICA 0039-3223 1730-6337 246 (2) pp. 133-166 2019
  • SJR Scopus - Mathematics (miscellaneous): Q2
    For a power bounded or polynomially bounded operator T sufficient conditions for the existence of a nontrivial hyperinvariant subspace are given. These hyperinvariant subspaces are the closures of the range of phi(T), where phi is a singular inner function if T is polynomially bounded, or phi is a function analytic in the unit disc with absolutely summable Taylor coefficients and singular inner part if T is supposed to be only power bounded. Also, an example of a quasianalytic contraction T is given such that the quasianalytic spectral set of T is not the whole unit circle T, while sigma(T) = T. The proofs are based on results by Esterle, Kellay, Borichev and Volberg.
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    2021-10-23 10:14