A sharp operator version of the Bishop-Phelps theorem for operators from to CL-spaces

Authors:
Lixin Cheng, Duanxu Dai and Yunbai Dong

Journal:
Proc. Amer. Math. Soc. **141** (2013), 867-872

MSC (2010):
Primary 47B37, 46B25; Secondary 47A58, 46B20

Published electronically:
December 6, 2012

MathSciNet review:
3003679

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Abstract | References | Similar Articles | 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 Bishop-Phelps theorem holds for bounded operators from to the space . In this note, we give two new examples of spaces having the AHSP: the almost CL-spaces 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 CL-spaces.

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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:
https://doi.org/10.1090/S0002-9939-2012-11326-7

Keywords:
Norm-attaining operator,
Bishop-Phelps theorem,
CL-space,
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.