Weighted Banach spaces of analytic functions with sup-norms and operators between them: a survey
José Bonet
2022Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas17 citationsDOIOpen Access PDF
Abstract
Abstract 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.
Topics & Concepts
MathematicsPure mathematicsOperator theoryBanach spaceCompact spaceFinite-rank operatorSpectrum (functional analysis)Analytic functionCompact operator on Hilbert spaceDiscrete mathematicsCompact operatorExtension (predicate logic)Computer scienceQuantum mechanicsPhysicsProgramming languageHolomorphic and Operator TheoryAdvanced Banach Space TheoryDifferential Equations and Boundary Problems