The Daugavetian index of a Banach space
type: Item
instance of: scholarly article
title: The Daugavetian index of a Banach space
zbMATH Open document ID: 1046.46009
published in: Taiwanese Journal of Mathematics
publication date: 2004-03-29T00:00:00Z
review text: The author defines the Daugavetian index \(\text{daug}\;X\) of a Banach space as the biggest constant \(m\) such that \(\| \text{ Id}+T\| \geq 1+m\| T\| \) for all compact operators on~\(X\). The case \(m=1\) is equivalent to the Daugavet property of \(X\) introduced by \textit{V.~Kadets, R.~V. Shvidkoy, G.~G. Sirotkin} and \textit{D.~Werner} [Trans. Am. Math. Soc. 352, 855--873 (2000; Zbl 0938.46016)]. Here, the Daugavetian index is characterised in terms of numerical ranges, and some stability properties are proved; e.g., \(\text{daug}\;C(K,X)\) is the maximum of \(\text{daug}\;C(K)\) and \(\text{daug}\;X\).
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 2063075
zbMATH Keywords: Daugavet property
zbMATH Keywords: Daugavet index
zbMATH Keywords: numerical range
zbMATH Keywords: stability
author: Miguel Martín
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407582
OpenAlex ID: W4242599994
DOI: 10.11650/TWJM/1500407582
description: scientific article; zbMATH DE number 2063075