Linear polynomial approximation schemes in Banach holomorphic function spaces

被引：9

作者：

Mashreghi, Javad ^{[1
]}

Ransford, Thomas ^{[1
]}

机构：

[1] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2019年 / 9卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Holomorphic function; Banach space; Polynomial; Bounded approximation property;

D O I：

10.1007/s13324-019-00312-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a Banach holomorphic function space on the unit disk. A linear polynomial approximation scheme for X is a sequence of bounded linear operators Tn:X -> X with the property that, for each f is an element of X, the functions Tn(f) are polynomials converging to f in the norm of the space. We completely characterize those spaces X that admit a linear polynomial approximation scheme. In particular, we show that it is not sufficient merely that polynomials be dense in X.

引用

页码：899 / 905

页数：7

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