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Three-space Problems for the Bounded Compact Approximation Property

Three-space Problems for the Bounded Compact Approximation Property
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摘要 In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p. In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.
作者 Dong Yang CHEN Ben Tuo ZHENG
机构地区 School of Mathematical Sciences Department of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第4期625-632,共8页 数学学报（英文版）
基金 supported by National Natural Science Foundation of China(Grant Nos.10526034 and 10701063) the Fundamental Research Funds for the Central Universities(Grant No.2011121039) supported by NSF(Grant Nos.DMS-0800061 and DMS-1068838)
关键词 The bounded compact approximation property a pair the （bounded） approximationproperty of order p The bounded compact approximation property, a pair, the （bounded） approximationproperty of order p
分类号 O177 [理学—基础数学]
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参考文献13

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Acta Mathematica Sinica,English Series
2013年 第4期

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