论文标题
关于投射张量产品的紧凑性弱
On weak compactness in projective tensor products
论文作者
论文摘要
我们研究了在Banach空间的投射张量产品中强烈紧凑地产生（以及一些亲戚）的特性。我们的主要结果如下。令$ 1 <p，q <\ infty $为$ 1/p+1/q \ geq 1 $。令$ x $（resp。，$ y $）为Banach空间，具有可计数的无条件有限维型schauder分解，具有偏低的较低$ p $ estimate（分别，$ q $ estimate）。如果$ x $和$ y $是强烈的紧凑生成的，那么其投射张量产品$ x \ wideHat {\ otimes}_πy$也是如此。
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 $1<p,q<\infty$ 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 its projective tensor product $X \widehat{\otimes}_πY$.
