@inbook{03a28ead9c3c4f7089e51ccf383333c2,

title = "Nonminimal cyclic invariant subspaces of hyperbolic composition operators",

abstract = "Operators on function spaces acting by composition to the right with a fixed self-map ϕ are called composition operators. We denote them Cϕ. Given ϕ, a hyperbolic disc automorphism, the composition operator Cϕ on the Hilbert Hardy space H2 is considered. The bilateral cyclic invariant subspaces Kf, f ∈ H2, of Cϕ are studied, given their connection with the invariant subspace problem, which is still open for Hilbert space operators. We prove that nonconstant inner functions u induce non–minimal cyclic subspaces Ku if they have unimodular, orbital, cluster points. Other results about Ku when u is inner are obtained. If f ∈ H2 \ {0} has a bilateral orbit under Cϕ, with Ces{\`a}ro means satisfying certain boundedness conditions, we prove Kf is non–minimal invariant under Cϕ. Other results proving the non–minimality of invariant subspaces of Cϕ of type Kf when f is not an inner function are obtained as well.",

keywords = "Composition operators, Invariant subspaces",

author = "Valentin Matache",

note = "Publisher Copyright: {\textcopyright} 2017 V. Matache.",

year = "2017",

doi = "10.1090/conm/699/14094",

language = "English (US)",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "247--262",

booktitle = "Contemporary Mathematics",

address = "United States",

}