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The approximation properties determined by operator ideals.
- Source :
- Acta Mathematica Sinica; Mar2017, Vol. 33 Issue 3, p311-326, 16p
- Publication Year :
- 2017
-
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 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 33
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 121251637
- Full Text :
- https://doi.org/10.1007/s10114-016-6009-y