Weakly compact operators onH∞

被引：0

作者：

Manuel D. Contreras

Santiago Díaz

机构：

[1] Universidad de Sevilla,Departamento de Matemática Aplicada II Escuela Superior de Ingenieros

来源：

Integral Equations and Operator Theory | 1999年 / 33卷

关键词：

Primary 46B25; 47A15; Secondary 32A35; 46B08; 46E15;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove that a weakly compact operator fromH∞ or any of its even duals into an arbitrary Banach space is uniformly convexifying. By using this, we establish three dicothomies: (1) every operator defined onH∞ or any of its even duals either fixes a copy ofl∞ or factors through a Banach space having the Banach-Saks property; (2) every quotient ofH∞ or any of its even duals either contains a copy ofl∞ or is super-reflexive; (3) every subspace ofL1/H01 or any of its even duals either contains a complemented copy ofl1 or is super-reflexive.

引用

页码：381 / 388

页数：7

共 15 条

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