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

被引：7
|
作者：
Bonet, Jose [1 ]
机构：
[1] Univ Politecn Valencia, Inst Matemat Pura & Aplicada, Valencia 46022, Spain
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 04期
关键词：
Weighted Banach spaces of holomorphic functions; Associated weights; Composition operators; Integral operators; Mean ergodic operators; Hypercyclic operators; COMPACT COMPOSITION OPERATORS; SUPERPOSITION OPERATORS; INTEGRATION OPERATORS; VOLTERRA OPERATORS; HOLOMORPHIC-FUNCTIONS; SOLID HULLS; DIFFERENTIATION OPERATOR; BERGMAN PROJECTIONS; CLASSICAL OPERATORS; INVARIANT SUBSPACES;
D O I：
10.1007/s13398-022-01323-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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, Cesaro 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.
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页数：40
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