On lifting the approximation property from a Banach space to its dual
HTML articles powered by AMS MathViewer
- by Åsvald Lima PDF
- Proc. Amer. Math. Soc. 143 (2015), 213-217 Request permission
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.References
- J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964
- William B. Johnson and Timur Oikhberg, Separable lifting property and extensions of local reflexivity, Illinois J. Math. 45 (2001), no. 1, 123–137. MR 1849989
- Åsvald Lima and Vegard Lima, Geometry of spaces of compact operators, Ark. Mat. 46 (2008), no. 1, 113–142. MR 2379687, DOI 10.1007/s11512-007-0060-y
- Åsvald Lima, Vegard Lima, and Eve Oja, Bounded approximation properties in terms of $C[0,1]$, Math. Scand. 110 (2012), no. 1, 45–58. MR 2900069, DOI 10.7146/math.scand.a-15195
- Åsvald Lima and Eve Oja, The weak metric approximation property, Math. Ann. 333 (2005), no. 3, 471–484. MR 2198796, DOI 10.1007/s00208-005-0656-0
- Eve Oja, The impact of the Radon-Nikodým property on the weak bounded approximation property, RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 100 (2006), no. 1-2, 325–331 (English, with English and Spanish summaries). MR 2267414
- Eve Oja, Lifting of the approximation property from Banach spaces to their dual spaces, Proc. Amer. Math. Soc. 135 (2007), no. 11, 3581–3587. MR 2336573, DOI 10.1090/S0002-9939-07-08996-4
- Eve Oja, Inner and outer inequalities with applications to approximation properties, Trans. Amer. Math. Soc. 363 (2011), no. 11, 5827–5846. MR 2817411, DOI 10.1090/S0002-9947-2011-05241-4
- Timur Oikhberg and Haskell P. Rosenthal, Extension properties for the space of compact operators, J. Funct. Anal. 179 (2001), no. 2, 251–308. MR 1809112, DOI 10.1006/jfan.2000.3674
Additional Information
- Åsvald Lima
- Affiliation: Department of Mathematics, University of Agder, Serviceboks 422, N-4604 Kristiansand, Norway
- Email: Asvald.Lima@uia.no
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3272746