关于射影张量积的弱紧性

IF 0.6 4区数学 Q3 MATHEMATICS

Quarterly Journal of Mathematics Pub Date : 2022-11-29 DOI:10.1093/qmath/haac036

José Rodríguez

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引用次数: 0

摘要

研究了Banach空间的射影张量积的强弱紧生成(及其相关性质)。我们的主要结果如下。让$1 \unicode{x003C} p,q\unicode{x003C}\infty$变成$1/p+1/q\geq 1$。设X。， Y)是一个Banach空间，该空间具有一个不相交的低p估计(p < 0.05)的可数无条件有限维Schauder分解。， q-estimate)。如果X和Y是强弱紧生成的，那么它们的射影张量积$X {\widehat{\otimes}_\pi} Y$也是。

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On weak compactness in projective tensor products

We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1 \unicode{x003C} p,q\unicode{x003C}\infty$ be such that $1/p+1/q\geq 1$. Let X (resp., Y) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower p-estimate (resp., q-estimate). If X and Y are strongly weakly compactly generated, then so is their projective tensor product $X {\widehat{\otimes}_\pi} Y$.

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来源期刊

Quarterly Journal of Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.