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The weak bounded approximation property of pairs

Authors: Dongyang Chen, Ju Myung Kim and Bentuo Zheng
Journal: Proc. Amer. Math. Soc. 143 (2015), 1665-1673
MSC (2010): Primary 46B28; Secondary 47L20
Published electronically: November 4, 2014
MathSciNet review: 3314079
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Abstract: We study the weak bounded approximation property (weak BAP) of pairs and show that each of the spaces $ c_0$ and $ \ell _1$ has a subspace having the approximation property but failing the weak BAP.

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Additional Information

Dongyang Chen
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

Ju Myung Kim
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul, 151-747, Korea

Bentuo Zheng
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152-3240

Keywords: Approximation property, bounded approximation property, weak bounded approximation property
Received by editor(s): January 7, 2013
Received by editor(s) in revised form: August 13, 2013, and September 12, 2013
Published electronically: November 4, 2014
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (Grant No. 10701063) and the Fundamental Research Funds for the Central Universities (Grant No. 2011121036)
The second author, who was the corresponding author, was supported by NRF Grant 2013R1A1A2A10058087, funded by the Korean Government
The third author was partially supported by NSF-DMS-1200370.
The authors were participants in the NSF Workshop in Analysis and Probability, Texas A&M University (2012)
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society

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