On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces
Volume 144 / 2001
Studia Mathematica 144 (2001), 275-295
MSC: 46B20, 46E30, 46A45, 46B25.
DOI: 10.4064/sm144-3-5
Abstract
Some relations between the James (or non-square) constant $J(X)$ and the Jordan–von Neumann constant $C_{\rm NJ}(X)$, and the normal structure coefficient $N(X)$ of Banach spaces $X$ are investigated. Relations between $J(X)$ and $J(X^*)$ are given as an answer to a problem of Gao and Lau [16]. Connections between $C_{\rm NJ}(X)$ and $J(X)$ are also shown. The normal structure coefficient of a Banach space is estimated by the $C_{\rm NJ}(X)$-constant, which implies that a Banach space with $C_{\rm NJ}(X)$-constant less than 5/4 has the fixed point property.
