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

Authors:	Antonio Jimé nez-Melado Enrique Llorens-Fuster Satit Saejung

Institution:	Departamento de Análisis Matemático, Universidad de Málaga, Facultad de Ciencias, 29071 Málaga, Spain ; Departamento de Análisis Matemático, Facultad de Matemáticas, 46100 Burjassot, Valencia, Spain ; Department of Mathematics, Khon Kaen University, Khon Kaen, 40002, Thailand

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.

Keywords:	von Neumann-Jordan constant James constant normal structure

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