On the von Neumann-Jordan constant for Banach spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the von Neumann-Jordan constant for Banach spaces

Authors:	Mikio Kato Yasuji Takahashi

Institution:	Department of Mathematics, Kyushu Institute of Technology, Tobata, Kitakyushu 804, Japan Yasuji Takahashi ; Department of System Engineering, Okayama Prefectural University, Soja 719-11, Japan

Abstract:	Let $C_{\mathrm {NJ}} (E)$ be the von Neumann-Jordan constant for a Banach space . It is known that $1\le C_{\mathrm {NJ}}(E)\le 2$ for any Banach space ; and is a Hilbert space if and only if $C_{\mathrm {NJ}} (E)=1$ . We show that: (i) If is uniformly convex, $C_{\mathrm {NJ}} (E)$ is less than two; and conversely the condition $C_{\mathrm {NJ}} (E)<2$ implies that admits an equivalent uniformly convex norm. Hence, denoting by $\widetilde C_{\mathrm {NJ}} (E)$ the infimum of all von Neumann-Jordan constants for equivalent norms of , is super-reflexive if and only if $\widetilde C_{\mathrm {NJ}} (E)<2$ . (ii) If $\widetilde C_{\mathrm {NJ}} (E)=2^{2/p-1}$ , $1<p\le 2$ (the same value as that of -space), is of Rademacher type and cotype for any with $1\le r<p$ , where ; the converse holds if is a Banach lattice and is finitely representable in or .

Keywords:	von Neumann-Jordan constant uniform convexity super-reflexivity type and cotype finite representability $p$-convexity and $p$-concavity for a Banach lattice

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏