Denting and strongly extreme points in the unit ball of spaces of operators
type: Item
instance of: scholarly article
title: Denting and strongly extreme points in the unit ball of spaces of operators
zbMATH Open document ID: 0943.46006
DOI: 10.1007/BF02837769
author: T.S.S.R.K. Rao
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2000-08-28T00:00:00Z
review text: The following are the main results of this interesting paper: (1) There are no denting points in the unit ball of \(\mathcal L(\ell^p,Y)\) whenever there is a non-compact operator and the space of compact operators \(\mathcal K(\ell^p,Y)\) is an M-ideal in \(\mathcal L(\ell^p,Y)\). (2) The unit ball of the space \(\mathcal L(L^1(\mu),X)\) has a point of weak-norm continuity iff \(L^1(\mu)\) is finite dimensional and the unit ball of X has a point of weak-norm continuity. (3) There are no points of weak-norm continuity in the unit ball of \(\mathcal L(X,C(K))\), where \(K\) is an infinite, totally disconnected compact Hausdorff space. (4) Suppose \(X^*\) has the extreme point intersection property (i.e., \(|x*(x)|\) = 1 for all \(x \in \delta_e X_1\) and all \(x* \in \delta_eX*_1\)). Then any `nice' operator \(T\) in the unit ball of \(\mathcal L(X,Y)\) (i.e., \(T*(\delta_eB(Y*)) \subset \delta_eB(X*)\), where B denotes the unit ball of the space indicated) is a strongly extreme point.
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1340037
zbMATH Keywords: denting point
zbMATH Keywords: strongly extreme point
zbMATH Keywords: \(M\)-ideal
zbMATH Keywords: point of weak-norm continuity
reviewed by: Srinivasa Swaminathan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02837769
OpenAlex ID: W2087205686
description: scientific article; zbMATH DE number 1340037