The Three-Space Problem for L 1
The Three-Space Problem for L 1
复制标题
L 1 的三空间问题
DOI：
10.2307/1990983
复制
发表时间：
1990
影响因子：
3.9
通讯作者：
M. Talagrand
中科院分区：
文献类型：
--
作者：
M. Talagrand
我们构造L1的一个子空间X，使X是同构于11的空间的1 -和，但使L1/X不包含L1的副本。我们还构造了两个巴拿赫空间E1， E2，它们不包含LI的副本，但使得E1 x E2包含L1的副本。此外，该内容下载于207.46.13.150 （Thu, 28 Jul 2016 05:31:04 UTC）的投影均使用http://about.jstor.org/terms。LI的L' 29的三维问题在每个因素上是一对一的，并且L1的单位球的图像是封闭的。这些例子解决了J. Lindenstrauss， P. Pelczynski， J. Bourgain和H. P. Rosenthal的问题。equipment D' analyzer - tour 46, u.a.au C.N.R.S. no . 754, UNIVERSITt PARIS VI, 4 PLACE JUSSIEU, 75230 PARIS CEDEX 05， OHIO STATE UNIVERSITY OF数学系，231 w18 AVENUE， COLUMBUS， OHIO 43210本内容从207.46.13.150（星期四，2016年7月28日，05:31:04 UTC）下载
We construct a subspace X of L1 such that X is an 1 -sum of spaces isomorphic to 11 but such that L1/X does not contain a copy of L1. We also construct two Banach spaces E1, E2 that do not contain a copy of LI but such that E1 x E2 contains a copy of L1 . Moreover, the projections This content downloaded from 207.46.13.150 on Thu, 28 Jul 2016 05:31:04 UTC All use subject to http://about.jstor.org/terms THE THREE-SPACE PROBLEM FOR L' 29 of LI on each factor are one-to-one, and the images of the unit ball of L1 are closed. These examples settle questions of J. Lindenstrauss, P. Pelczynski, J. Bourgain, and H. P. Rosenthal. EQUIPE D'ANALYSE-TOUR 46, U.A. AU C.N.R.S. N0 754, UNIVERSITt PARIS VI, 4 PLACE JUSSIEU, 75230 PARIS CEDEX 05 DEPARTMENT OF MATHEMATICS, OHIO STATE UNIVERSITY, 231 W. 18TH AVENUE, COLUMBUS, OHIO 43210 This content downloaded from 207.46.13.150 on Thu, 28 Jul 2016 05:31:04 UTC All use subject to http://about.jstor.org/terms