Journal of Inequalities and Applications
Volume 2 (1998), Issue 1, Pages 89-97
Von Neumann–Jordan constant for Lebesgue–Bochner spaces
1Department of Mathematics, Kyushu Institute of Technology, Tobata, Kitakyushu 804, Japan
2Department of System Engineering, Okayama Prefectural University, Soja 719-11, Japan
Received 10 February 1997; Revised 23 May 1997
Copyright © 1998 Mikio Kato and Yasuji Takahashi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The von Neumann–Jordan (NJ-) constant for Lebesgue–Bochner spaces is determined under some conditions on a Banach space . In particular the NJ-constant for as well as (the space of -Schatten class operators) is determined. For a general Banach space we estimate the NJ-constant of , which may be regarded as a sharpened result of a previous one concerning the uniform non-squareness for . Similar estimates are given for Banach sequence spaces (-sum of Banach spaces ), which gives a condition by NJ-constants of ’s under which is uniformly non-square. A bi-product concerning ‘Clarkson’s inequality’ for and is also given.