We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach spac...We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach space X has the approximation property with respect to Ad whenever X＊ has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.展开更多
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....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.展开更多
基金supported by the Natural Science Foundation of Fujian Province of China(Grant No.2015J01026)supported by the NSF of China(Grant No.11301285)
文摘We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal ,4, that is, a Banach space X has the approximation property with respect to Ad whenever X＊ has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.
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)
文摘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.
