论文标题
关于在张量产品空间中达到规范的几篇评论
Several remarks on norm attaining in tensor product spaces
论文作者
论文摘要
本说明的目的是获得有关何时强烈差异的探测张量产品的标准的结果。我们证明，如果$ x \ hat {\ otimes}_πy$是强烈的可分割性，并且$ x $或$ y $具有度量近似属性，则每个有界的运算符，从$ x $到$ y^*$是紧凑的。我们还证明$（\ ell_p（i）\ hat {\ otimes}_π\ ell_q（j））^*$具有$ w^*$ - kadec-klee属性，每一个非空的套件$ i，j $，尤其是$ 2 <p，q <p，q <\ f infty $ $ \ ell_p（i）\ hat {\ otimes}_π\ ell_q（j）$是强烈的分散性。这扩展了Dantas，Kim，Lee和Mazzitelli的几个结果。我们还找到了空间$ x $和$ y $的示例，其中$ x \ pten y $中的规范张量很密集，但其补充也很密集。
The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if $X\hat{\otimes}_πY$ is strongly subdifferentiable and either $X$ or $Y$ has the metric approximation property then every bounded operator from $X$ to $Y^*$ is compact. We also prove that $(\ell_p(I)\hat{\otimes}_π\ell_q(J))^*$ has the $w^*$-Kadec-Klee property for every non-empty sets $I,J$ and every $2<p,q<\infty$, obtaining in particular that the norm of the space $\ell_p(I)\hat{\otimes}_π\ell_q(J)$ is strongly subdifferentiable. This extends several results of Dantas, Kim, Lee and Mazzitelli. We also find examples of spaces $X$ and $Y$ for which the set of norm-attaining tensors in $X\pten Y$ is dense but whose complement is dense too.
