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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lifting of the approximation property from Banach spaces to their dual spaces


Author: Eve Oja
Journal: Proc. Amer. Math. Soc. 135 (2007), 3581-3587
MSC (2000): Primary 46B20, 46B28, 47L05.
Published electronically: June 22, 2007
MathSciNet review: 2336573
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Abstract: Inspired by the principle of local reflexivity, due to Lindenstrauss and Rosenthal, a new geometric property of Banach spaces, the extendable local reflexivity, was recently introduced by Rosenthal. Johnson and Oikhberg proved that the extendable local reflexivity permits lifting the bounded approximation property from Banach spaces to their dual spaces. It is not known whether the extendable local reflexivity permits lifting the approximation property. We prove that it does whenever the space is complemented in its bidual. This involves the concept of the weak bounded approximation property, introduced by Lima and Oja.


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Additional Information

Eve Oja
Affiliation: Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE-50409 Tartu, Estonia
Email: eve.oja@ut.ee

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08996-4
PII: S 0002-9939(07)08996-4
Keywords: Approximation properties, extendable local reflexivity, projective tensor product of Banach spaces.
Received by editor(s): August 10, 2006
Published electronically: June 22, 2007
Additional Notes: This research was partially supported by Estonian Science Foundation Grant 5704
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.