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
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.
