A sharp operator version of the BishopPhelps theorem for operators from to CLspaces
Authors:
Lixin Cheng, Duanxu Dai and Yunbai Dong
Journal:
Proc. Amer. Math. Soc. 141 (2013), 867872
MSC (2010):
Primary 47B37, 46B25; Secondary 47A58, 46B20
Published electronically:
December 6, 2012
MathSciNet review:
3003679
Fulltext PDF
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References 
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Additional Information
Abstract: Acosta et al. in 2008 gave a characterization of a Banach space (called an approximate hyperplane series property, or AHSP for short) guaranteeing exactly that a quantitative version of the BishopPhelps theorem holds for bounded operators from to the space . In this note, we give two new examples of spaces having the AHSP: the almost CLspaces and the class of Banach spaces whose dual is uniformly strongly subdifferentiable on some boundary of . We then calculate the precise parameters associated to almost CLspaces.
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Additional Information
Lixin Cheng
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email:
lxcheng@xmu.edu.cn
Duanxu Dai
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email:
dduanxu@163.com
Yunbai Dong
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China
Email:
Baiyunmu301@126.com
DOI:
http://dx.doi.org/10.1090/S000299392012113267
Keywords:
Normattaining operator,
BishopPhelps theorem,
CLspace,
Banach space
Received by editor(s):
January 21, 2011
Received by editor(s) in revised form:
June 17, 2011, June 23, 2011, June 25, 2011, and June 27, 2011
Published electronically:
December 6, 2012
Additional Notes:
The first author was supported by the Natural Science Foundation of China, grant 11771201.
Communicated by:
Thomas Schlumprecht
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
