A Characterization of Banach Spaces Containing l1
A Characterization of Banach Spaces Containing l1
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DOI：
10.1073/pnas.71.6.2411
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发表时间：
1974-06
影响因子：
11.1
通讯作者：
H. Rosenthal
中科院分区：
文献类型：
--
作者：
H. Rosenthal
证明了Banach空间包含同构于l1的子空间当（且仅当）它有一个不含弱柯西子列的有界序列。证明结果表明，一个给定集合的子集序列有一个子序列，要么是收敛的或布尔独立的。
Abstract It is proved that a Banach space contains a subspace isomorphic to l1 if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.