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RESEARCH PRODUCT

Mean ergodic composition operators on Banach spaces of holomorphic functions

Enrique JordáM. Carmen Gómez-colladoDavid JornetMaría J. Beltrán-meneu

subject

Pure mathematicsEndomorphismComposition operatorBanach spaceHolomorphic functionDisc algebra01 natural sciencesMean ergodic operatorFOS: Mathematics47B33 47A35 46E15Ergodic theoryComplex Variables (math.CV)0101 mathematicsMathematicsMathematics::Functional AnalysisDenjoy Wolff pointMathematics - Complex VariablesMathematics::Complex Variables010102 general mathematicsComposition (combinatorics)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsIterated functionComposition operatorMATEMATICA APLICADAUnit (ring theory)Analysis

description

[EN] Given a symbol cc, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C-phi(f) = f circle phi defined on the Banach spaces of holomorphic functions A(D) and H-infinity(D). We obtain different conditions on the symbol phi which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behavior of the iterates of the symbol. Finally, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.

yearjournalcountryeditionlanguage
2016-01-13Journal of Functional Analysis
https://doi.org/10.1016/j.jfa.2016.03.003