Boundedness of Volterra operators on spaces of entire functions

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

2022

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.

Section: Volterra Operatorsmentioning

confidence: 99%

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

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

2022

“…and dA denotes the usual Lebesgue area measure on C. These spaces have been studied in various contexts; see for instance [4,6,9,17].…”

Section: Introductionmentioning

confidence: 99%

Mean ergodic composition operators on generalized Fock spaces

Seyoum

Mengestie

2019

RACSAM

Every bounded composition operator C ψ dened by an analytic symbol ψ on the complex plane when acting on generalized Fock spaces F p ϕ , 1 ≤ p ≤ ∞, is power bounded. Mean ergodic and uniformly mean ergodic composition operators on the spaces are characterized. The set of periodic points of these operators is also determined. Theorem 1.1. (Theorem 2.1 of [18], Theorem 2.1 of [19]) Let 1 ≤ p ≤ ∞ and ψ be a nonconstant analytic map on the complex plane C. Then the operator C ψ : F p ϕ → F p ϕ is 1 *Corresponding author Key words and phrases. Composition operators, generalized Fock spaces, power bounded operator, mean ergodic operator, uniformly mean ergodic operator.

Associated weights for spaces ofp-integrable entire functions

Quaestiones Mathematicae

Mangino

2019

In analogy to the notion of associated weights for weighted spaces of analytic functions with sup-norms, p-associated weights are introduced for spaces of entire p-integrable functions, 1 ≤ p < ∞. As an application, necessary conditions for the boundedness of composition operators acting between general Fock type spaces are proved. Notation and preliminariesConsider the space C N endowed with the complex inner product and the norm defined by: