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 $c_0$.

• 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