Dynamics of Weighted Composition Operators on Spaces of Entire Functions of Exponential and Infraexponential Type

Abstract

Given an affine symbol $$\varphi $$ φ and a multiplier w, we focus on the weighted composition operator $$C_{w, \varphi }$$ C w , φ acting on the spaces Exp and $$Exp^0$$ E x p 0 of entire functions of exponential and of infraexponential type, respectively. We characterize the continuity of the operator and, for w the product of a polynomial by an exponential function, we completely characterize power boundedness and (uniform) mean ergodicity. In the case of multiples of composition operators, we also obtain the spectrum and characterize hypercyclicity.

Mean ergodic weighted shifts on Köthe echelon spaces

“…, respectively. In particular, property (11) is satisfied so that Λ ∞ (α) and Λ 0 (α) are both Montel spaces. (i) Assume that B w is continuous in Λ ∞ (α).…”

“…[1,2,3,4], [12], [30,31]) as well as for concrete types of continuous linear operators (see e.g. [5], [6], [7], [8], [9,10], [11], [13,14], [15], [16], [19], [20], [21], [23,24], [25,26], [27], [32], [33]).…”

Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey

“…Moreover, in the case of affine symbols and exponential weights, it is analyzed when the operator is power bounded, (uniformly) mean ergodic and hypercyclic. This work was continued by Beltrán and Jordá [29] to investigate power boundedness, (uniform) mean ergodicity and hypercyclicity of certain weighted composition operators on spaces of entire functions of exponential and infraexponential type.…”

Dynamics of composition operators on function spaces defined by local and global properties

“…For further results on mean ergodic operators we refer to [19,22]. For recent results on mean ergodic operators in lcHs' we refer to [1][2][3][4]7,12,17], for example, and the references therein.…”