The Grothendieck property for injective tensor products of Banach spaces

被引：0

作者：

Donghai Ji

Xiaoping Xue

Qingying Bu

机构：

[1] Harbin University of Science and Technology,Department of Mathematics

[2] Harbin Institute of Technology,Department of Mathematics

[3] University of Mississippi,Department of Mathematics

来源：

Czechoslovak Mathematical Journal | 2010年 / 60卷

关键词：

Banach space; Grothendieck property; tensor product; 46B28; 46M05;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let X be a Banach space with the Grothendieck property, Y a reflexive Banach space, and let X ⊗̌ɛY be the injective tensor product of X and Y. If either X** or Y has the approximation property and each continuous linear operator from X* to Y is compact, then X ⊗̌ɛY has the Grothendieck property.In addition, if Y has an unconditional finite dimensional decomposition, then X ⊗̌ɛY has the Grothendieck property if and only if each continuous linear operator from X* to Y is compact.

引用

页码：1153 / 1159

页数：6

共 6 条

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[5]

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[6]

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