On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces

Mikio Kato¹ ; Lech Maligranda² ; Yasuji Takahashi³

¹ Department of Mathematics Kyushu Institute of Technology Tobata, Kitakyushu 804-8550, Japan
² Department of Mathematics Luleå University of Technology S-971 87 Luleå, Sweden
³ Department of System Engineering Okayama Prefectural University Soja 719-1197, Japan

Studia Mathematica, Tome 144 (2001) no. 3, pp. 275-295

Résumé

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.

Détail

DOI : 10.4064/sm144-3-5

Mots-clés : relations between james non square constant jordan von neumann constant normal structure coefficient banach spaces investigated relations between * given answer problem gao lau connections between shown normal structure coefficient banach space estimated constant which implies banach space constant has fixed point property