Let T be an absolutely continuous polynomially bounded operator, and let θ be a singular inner function. It is shown that if θ(T ) is invertible and some additional conditions are fulfilled, then T has nontrivial hyperinvariant subspaces.2010 Mathematics Subject Classification. Primary 47A15; Secondary 47A60, 47A10.
For a power bounded or polynomially bounded operator T sufficient conditions for the existence of a nontrivial hyperinvariant subspace are given. The obtained hyperinvariant subspaces of T have the form of the closure of the range of ϕ(T ). Here ϕ is a singular inner function, if T is polynomially bounded, or ϕ is an analytic in the unit disc function with absolutely summable Taylor coefficients and singular inner part, if T is supposed to be power bounded only. 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 σ(T ) = T. Proofs are based on results by Esterle, Kellay, Borichev and Volberg.2010 Mathematics Subject Classification. Primary 47A15; Secondary 47A60, 47A10.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.