An extension of a simply inequality between von Neumann–Jordan and James constants in Banach spaces

An extension of a simply inequality between von Neumann–Jordan and James constants in Banach... For a non-trivial Banach space X, let J(X), C NJ(X), C NJ (p) (X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C NJ (p) (X) ≤ J(X) with p ≥ 2, which covers the well-known inequality C NJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Sinica, English Series Springer Journals

An extension of a simply inequality between von Neumann–Jordan and James constants in Banach spaces

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Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Copyright
Copyright © 2017 by Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
1439-8516
eISSN
1439-7617
D.O.I.
10.1007/s10114-017-6211-6
Publisher site
See Article on Publisher Site

Abstract

For a non-trivial Banach space X, let J(X), C NJ(X), C NJ (p) (X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C NJ (p) (X) ≤ J(X) with p ≥ 2, which covers the well-known inequality C NJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.

Journal

Acta Mathematica Sinica, English SeriesSpringer Journals

Published: May 10, 2017

References

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