Abstract
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 A, that is, a Banach space X has the approximation property with respect to A d 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.
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We thank the referees for their time and comments.
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The first author is supported by the Natural Science Foundation of Fujian Province of China (Grant No. 2015J01026); the second author is supported by the NSF of China (Grant No. 11301285)
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Chen, D.Y., Li, L. The approximation properties determined by operator ideals. Acta. Math. Sin.-English Ser. 33, 311–326 (2017). https://doi.org/10.1007/s10114-016-6009-y
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DOI: https://doi.org/10.1007/s10114-016-6009-y