Mean Ergodic Composition Operators on Banach spaces of holomorphic functions

2016/01/13 by Beltrán, María José, Gómez, María del Carmen, Jordá, Enrique +1
#46E15 #47A35 #47B33 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1601.03353

Abstract

Given a symbol φ, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C_φ(f)=f∘φ defined on the Banach spaces of holomorphic functions A(\mathbbD) and H^∞(\mathbbD). We obtain different conditions on the symbol φ which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behaviour of the iterates of the symbol. As an appendix, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.

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