具有Gordon Lewis性质的巴拿赫空间的Maurey扩张问题的解及相关结构
The solution to the Maurey extension problem for Banach spaces with the Gordon Lewis property and related structures
摘要：
本文的主要结果是：若巴拿赫空间X具有从X的任意子空间到任意余型2的巴拿赫空间的有界算子扩张到X上的有界算子的性质，则$B(\ell_{\infty},X^*)=Π_2(\ell_{\infty},X^*)$ .如果另外X具有高斯平均性质，则它是类型2。这意味着如果X具有戈登-刘易斯性质（特别是X可以是巴拿赫格）或者如果X同构于有限余型的巴拿赫格的子空间，则同样的结论成立，从而解决了这些空间类的Maurey扩张性质。本文还详细研究了取值于$\ell_p$ -空间$1\le p<\infty$的扩张算子的性质。
英文摘要：
The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then $B(\ell_{\infty},X^*)=Π_2(\ell_{\infty},X^*)$. If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension property for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in $\ell_p$-spaces, $1\le p<\infty$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
