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Right and Left Weak Approximation Properties in Banach Spaces

Published:2009-03-01
Printed: Mar 2009
• Changsun Choi
• Ju Myung Kim
• Keun Young Lee
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Abstract

New necessary and sufficient conditions are established for Banach spaces to have the approximation property; these conditions are easier to check than the known ones. A shorter proof of a result of Grothendieck is presented, and some properties of a weak version of the approximation property are addressed.
 Keywords: approximation property, quasi approximation property, weak approximation property
 MSC Classifications: 46B28 - Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46B10 - Duality and reflexivity [See also 46A25]