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On lifting the approximation property from a Banach space to its dual


Author: Åsvald Lima
Journal: Proc. Amer. Math. Soc. 143 (2015), 213-217
MSC (2010): Primary 46B28; Secondary 46B20, 47L05
DOI: https://doi.org/10.1090/S0002-9939-2014-12208-8
Published electronically: August 28, 2014
MathSciNet review: 3272746
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Abstract: We prove that if a Banach space is extendably locally reflexive, then it is compactly locally reflexive. Using results by Lima and Lima, this implies that if a Banach space has the approximation property and is extendably locally reflexive, then its dual space has the approximation property.


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Additional Information

Åsvald Lima
Affiliation: Department of Mathematics, University of Agder, Serviceboks 422, N-4604 Kristiansand, Norway
Email: Asvald.Lima@uia.no

DOI: https://doi.org/10.1090/S0002-9939-2014-12208-8
Keywords: Banach spaces, approximation properties
Received by editor(s): March 5, 2013
Received by editor(s) in revised form: March 19, 2013
Published electronically: August 28, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society

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