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On the James and von Neumann-Jordan constants in Banach spaces

Author: Fenghui Wang
Journal: Proc. Amer. Math. Soc. 138 (2010), 695-701
MSC (2000): Primary 46B20
Published electronically: October 7, 2009
MathSciNet review: 2557186
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Abstract: Recently Alonso, Martín and Papini conjectured that the value of the von Neumann-Jordan constant is less than or equal to that of the James constant. This paper presents an affirmative answer to such a conjecture. Moreover, we obtain a sharp estimate for the von Neumann-Jordan constant.

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Fenghui Wang
Affiliation: Department of Mathematics, Luoyang Normal University, Luoyang 471022, People’s Republic of China

Keywords: Modulus of convexity, James constant, Neumann-Jordan constant
Received by editor(s): February 28, 2009
Received by editor(s) in revised form: July 1, 2009
Published electronically: October 7, 2009
Additional Notes: This work was supported by the Natural Science Foundation of the Department of Education, Henan (2008A110012), development programs in science and technology of Henan Province (092300410187), and the Youth Foundation of Luoyang Normal University (2008-QNJJ-011).
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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