On operators from separable reflexive spaceswith asymptotic structure
 作者： Bentuo Zheng 作者单位： 1Department of Mathematics The University of Texas at Austin 1 University Station C1200 Austin, TX 78712-0257, U.S.A. 刊名： Studia Mathematica, 2008, Vol.185 , pp.87-98 来源数据库： Institute of Mathematics Polish Academy of Sciences DOI： 10.4064/sm185-1-6 原始语种摘要： Let $1< q< p< \infty$ and $q\leq r\leq p$. Let $X$ be a reflexive Banach space satisfying a lower-$\ell_q$-tree estimate and let $T$ be a bounded linear operator from $X$ which satisfies an upper-$\ell_p$-tree estimate. Then $T$ factors through a subspace of $(\sum F_n)_{\ell_r}$, where $(F_n)$ is a sequence of finite-dimensional spaces. In particular, $T$ factors through a subspace of a reflexive space with an $(\ell_p, \ell_q)$ FDD. Similarly, let $1< q< r< p< \infty$ and let $X$ be a separable reflexive Banach space satisfying an asymptotic lower-$\ell_q$-tree estimate. Let $T$ be a bounded linear operator from $X$ which satisfies an asymptotic upper-$\ell_p$-tree estimate. Then $T$ factors through a subspaceof $(\sum G_n)_{\ell_r}$, where $(G_n)$ is a sequence of finite-dimensional... spaces.In particular, $T$ factors through a subspace of a reflexivespace with an asymptotic $(\ell_p, \ell_q)$ FDD.

• 话务员　细致的
• asymptotic　渐近的
• estimate　估计
• reflexive　自反的
• bounded　有界的
• particular　细致的
• operator　细致的
• separable　可分的
• through　经过
• subspace　子空间
• where　哪里