scholarly journals Volterra operators between limits of Bergman-type weighted spaces of analytic functions

2021 ◽  
pp. 1-14
Author(s):  
Ersin KIZGUT
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Volterra Operators ◽  
Spaces Of Analytic Functions

scholarly journals On M-ideals and o-O type spaces

2017 ◽  
Vol 121 (1) ◽  
pp. 151 ◽  
Author(s):  
Karl-Mikael Perfekt
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Function Spaces ◽  
Weighted Spaces ◽  
Bounded Mean Oscillation ◽  
Mean Oscillation ◽  
Type Spaces ◽  
Invariant Spaces ◽  
Holder Spaces ◽  
Spaces Of Analytic Functions

We consider pairs of Banach spaces $(M_0, M)$ such that $M_0$ is defined in terms of a little-$o$ condition, and $M$ is defined by the corresponding big-$O$ condition. The construction is general and pairs include function spaces of vanishing and bounded mean oscillation, vanishing weighted and weighted spaces of functions or their derivatives, Möbius invariant spaces of analytic functions, Lipschitz-Hölder spaces, etc. It has previously been shown that the bidual $M_0^{**}$ of $M_0$ is isometrically isomorphic with $M$. The main result of this paper is that $M_0$ is an M-ideal in $M$. This has several useful consequences: $M_0$ has Pełczýnskis properties (u) and (V), $M_0$ is proximinal in $M$, and $M_0^*$ is a strongly unique predual of $M$, while $M_0$ itself never is a strongly unique predual.

scholarly journals Whitney Decomposition, Embedding Theorems and Interpolation Questions in Weighted Spaces of Analytic Functions

2019 ◽  
Author(s):  
Ф.А. Шамоян ◽  
Е.В. Тасоева
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Embedding Theorems ◽  
Whitney Decomposition ◽  
Spaces Of Analytic Functions

По классической теореме Уитни каждое открытое множество на плоскости можно представить в виде объединения специальных квадратов, внутренности которых не пересекаются. В статье, используя эти свойства квадратов Уитни, вводится новое понятие: для каждого центра $a_k$ квадрата Уитни существует точка $a_k^*\in C/G$ такая, что расстояние до границы открытого множества $G$ заключается между двумя константами независимо от $k$. Используя свойства Уитни в~статье, в частности, устанавливается необходимое и достаточное условие на ${z_k }_1^{\infty}\subset G$, при котором оператор $R(f)=(f(z_1),f(z_2),\ldots,f(z_n),\ldots)$ отображает обобщенные плоские классы Неванлинны по множеству $G$ в $l^p.$

Complemented Submodules in Weighted Spaces of Analytic Functions

1992 ◽  
Vol 157 (1) ◽  
pp. 263-276 ◽  
Author(s):  
Michael Langenbruch ◽  
Siegfried Momm
Keyword(s):  
Analytic Functions ◽  
Weighted Spaces ◽  
Spaces Of Analytic Functions

scholarly journals Volterra operators and semigroups in weighted Banach spaces of analytic functions

2013 ◽  
Vol 65 (2) ◽  
pp. 233-249 ◽  
Author(s):  
Manuela Basallote ◽  
Manuel D. Contreras ◽  
Carmen Hernández-Mancera ◽  
María J. Martín ◽  
Pedro J. Paúl
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Volterra Operators ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions
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