A double-dual characterization of separable Banach spaces containingl1
A double-dual characterization of separable Banach spaces containingl1
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DOI：
10.1007/bf02760341
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发表时间：
1975-09
影响因子：
1
通讯作者：
E. Odell;H. Rosenthal
中科院分区：
文献类型：
--
作者：
E. Odell;H. Rosenthal
证明了可分Banach空间B包含同构于1的子空间当且仅当B的双对偶B ** 中存在一个元素，它不是B中元素列的弱 * 极限。因此，B包含f1的同构当（且仅当）B ** 的基数大于连续统的基数。
It is proved that a separable Banach spaceBcontains a subspace isomorphic tol1if (and only if) there exists an element inB**, the double-dual ofB, which is not a weak* limit of a sequence of elements inB. ConsequentlyBcontains an isomorph ofl1if (and only if) the cardinality ofB** is greater than that of the continuum.