Weak sequential completeness of spaces of homogeneous polynomials

被引：2

作者：

Bu, Qingying ^{[1
]}

Ji, Donghai ^{[2
]}

Wong, Ngai-Ching ^{[3
]}

机构：

[1] Univ Mississippi, Dept Math, University, MS 38677 USA

[2] Harbin Univ Sci & Technol, Dept Math, Harbin 150080, Peoples R China

[3] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 427卷 / 02期

关键词：

Homogeneous polynomials; Weak sequential completeness; Reflexivity; BANACH-SPACES; APPROXIMATION PROPERTY; COMPACT APPROXIMATION; HOLOMORPHIC MAPPINGS; TENSOR PRODUCT; REFLEXIVITY; DUALITY; THEOREM;

D O I：

10.1016/j.jmaa.2015.02.078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P-w(E-n; F) be the space of all continuous n-homogeneous polynomials from a Banach space E into another F, that are weakly continuous on bounded sets. We give sufficient conditions for the weak sequential completeness of P-w, (E-n; F). These sufficient conditions are also necessary if both E* and F have the bounded compact approximation property. We also show that the weak sequential completeness and the reflexivity of P-w (E-n; F) are equivalent whenever both E and F are reflexive. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1119 / 1130

页数：12

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