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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The von Neumann-Jordan constant, weak orthogonality and normal structure in Banach spaces


Authors: Antonio Jiménez-Melado, Enrique Llorens-Fuster and Satit Saejung
Journal: Proc. Amer. Math. Soc. 134 (2006), 355-364
MSC (2000): Primary 46B20
Published electronically: September 21, 2005
MathSciNet review: 2176002
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Abstract: We give some sufficient conditions for normal structure in terms of the von Neumann-Jordan constant, the James constant and the weak orthogonality coefficient introduced by B. Sims. In the rest of the paper, the von Neumann-Jordan constant and the James constant for the Bynum space $\ell _{2,\infty}$ are computed, and are used to show that our results are sharp.


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Additional Information

Antonio Jiménez-Melado
Affiliation: Departamento de Análisis Matemático, Universidad de Málaga, Facultad de Ciencias, 29071 Málaga, Spain
Email: melado@uma.es

Enrique Llorens-Fuster
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, 46100 Burjassot, Valencia, Spain
Email: enrique.llorens@uv.es

Satit Saejung
Affiliation: Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand
Email: satitz@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08362-0
PII: S 0002-9939(05)08362-0
Keywords: von Neumann-Jordan constant, James constant, normal structure
Received by editor(s): January 23, 2004
Published electronically: September 21, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society