Two results on strong proximinality
type: Item
instance of: scholarly article
title: Two results on strong proximinality
zbMATH Open document ID: 1477.46010
author: T.S.S.R.K. Rao
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2021-07-29T00:00:00Z
review text: \textit{G.~Godefroy} and \textit{V.~Indumathi} [Rev. Mat. Complut. 14, No.~1, 105--125 (2001; Zbl 0993.46004)] proved that the kernel of a functional \(x^*\) is strongly proximinal if and only if the dual norm is strongly subdifferentiable at~\(x^*\); see [loc. cit.] or the present paper for unexplained notation. The author uses this characterisation to provide a criterion for a subspace \(Y\) of a Banach space \(X\) to be strongly proximinal and he uses it to give a quick proof (quick modulo [loc. cit.]) of the known result that \(M\)-ideals are strongly proximinal.
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 7376441
zbMATH Keywords: strongly proximinal subspace
zbMATH Keywords: strong subdifferentiability
zbMATH Keywords: SSD point
zbMATH Keywords: \(M\)-ideals
MaRDI profile type: Publication
full work available at URL: s12044-021-00613-y
OpenAlex ID: W3158761579
cites work: Structure in real Banach spaces. I and II
cites work: Survey of last ten years of work done in India in some selected areas of functional analysis and operator theory
cites work: Q5447314
cites work: Q5287885
cites work: Strong proximinality and polyhedral spaces
cites work: \(M\)-ideals in Banach spaces and Banach algebras
cites work: Strong proximinality and intersection properties of balls in Banach spaces
cites work: Some geometric properties of Read's space
cites work: Norm-attaining functionals need not contain 2-dimensional subspaces
cites work: Q5595759
DOI: 10.1007/S12044-021-00613-Y
description: scientific article; zbMATH DE number 7376441