# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 144 / 2001

Studia Mathematica 144(2001), 275-295 MSC: 46B20, 46E30, 46A45, 46B25. DOI: 10.4064/sm144-3-5

#### Streszczenie

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.

#### Autorzy

• Mikio KatoDepartment of Mathematics
Kyushu Institute of Technology
Tobata, Kitakyushu 804-8550, Japan
e-mail
Luleå University of Technology
S-971 87 Luleå, Sweden
e-mail
• Yasuji TakahashiDepartment of System Engineering
Okayama Prefectural University
Soja 719-1197, Japan
e-mail

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