On operators which factor through $l_p$ or $c_0$
作者: Bentuo Zheng
作者单位: 1Department of Mathematics Texas A&M University College Station, TX 77843, U.S.A.
刊名: Studia Mathematica, 2006, Vol.176 , pp.177-190
来源数据库: Institute of Mathematics Polish Academy of Sciences
DOI: 10.4064/sm176-2-5
原始语种摘要: Let $1< p< \infty$. Let $X$ be a subspace of a space $Z$ witha shrinking F.D.D. $(E_n)$ which satisfies a block lower-$p$estimate. Then any bounded linear operator $T$ from $X$ whichsatisfies an upper-$(C,p)$-tree estimate factors through asubspace of $(\sum F_n)_{l_p}$, where $(F_n)$ is a blocking of$(E_n)$. In particular, we prove that an operator from$L_p\, (2< p< \infty)$ satisfies an upper-$(C,p)$-treeestimate if and only if it factors through $l_p$. This gives ananswer to a question of W. B. Johnson. We also prove that if$X$ is a Banach space with $X^*$ separable and $T$ is anoperator from $X$ which satisfies anupper-$(C,\infty)$-estimate, then $T$ factors through a subspaceof $c_0$.
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  • or 或者
  • through 经过
  • estimate 估计
  • prove 实验
  • bounded 有界的
  • particular 细致的
  • question 问题
  • shrinking 收缩
  • Johnson 约翰逊
  • factor 因素