Von Neumann-Jordan constant of absolute normalized norms on \(\mathbb{C}^2\)
type: Item
instance of: scholarly article
title: Von Neumann-Jordan constant of absolute normalized norms on \(\mathbb{C}^2\)
zbMATH Open document ID: 0961.46008
author: Kichi-Suke Saito
author: Mikio Kato
author: Yasuji Takahashi
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-14T00:00:00Z
review text: The paper is devoted to the von Neumann-Jordan constant of a Banach space defined by \textit{J. A. Clarkson} [Ann. Math., II. Ser. 38, 114-115 (1937; Zbl 0016.03002)] as the smallest positive constant \(C\) such that \[ {1\over C}\leq {\|x+ y\|^2+\|x- y\|^2\over 2(\|x\|^2+\|y\|^2)}\leq C \] for every nonzero vectors \(x\) and \(y\) in the space. The authors estimated the von Neumann-Jordan constant for \(\mathbb{C}^2\) with norm satisfying the conditions: \[ \|(z,w)\|= \|(|z|,|w|)\|\quad\text{and} \quad \|(1,0)\|= \|(0,1)\|= 1. \] These estimates are used to find the exact values of the constants for some classes of spaces.
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B07
zbMATH DE Number: 1449221
zbMATH Keywords: von Neumann-Jordan constant
Wikidata QID: Q60060064
reviewed by: Mikhail Ostrovskii
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6727
OpenAlex ID: W1986183508
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DOI: 10.1006/JMAA.2000.6727
description: scientific article; zbMATH DE number 1449221