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...
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关键词翻译
关键词翻译
  • 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