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
… Show more
“…, 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).…”
Section: Resultsmentioning
confidence: 99%
“…[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]).…”
Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted forward shift operators, respectively, on Köthe echelon spaces in terms of the weight sequence and the Köthe matrix. These conditions are evaluated for the special case of power series spaces which allow for a characterization of said properties in many cases. In order to demonstrate the applicability of our conditions, we study the above properties for several classical operators on certain function 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).…”
Section: Resultsmentioning
confidence: 99%
“…[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]).…”
Necessary and sufficient conditions are given for mean ergodicity, power boundedness, and topologizability for weighted backward shift and weighted forward shift operators, respectively, on Köthe echelon spaces in terms of the weight sequence and the Köthe matrix. These conditions are evaluated for the special case of power series spaces which allow for a characterization of said properties in many cases. In order to demonstrate the applicability of our conditions, we study the above properties for several classical operators on certain function spaces.
“…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.…”
In this survey we report about recent work on weighted Banach spaces of analytic functions on the unit disc and on the whole complex plane defined with sup-norms and operators between them. Results about the solid hull and core of these spaces and distance formulas are reviewed. Differentiation and integration operators, Cesàro and Volterra operators, weighted composition and superposition operators and Toeplitz operators on these spaces are analyzed. Boundedness, compactness, the spectrum, hypercyclicity and (uniform) mean ergodicity of these operators are considered.
“…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.…”
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