Some problems in functional analysis inspired by Hahn-Banach type theorems
type: Item
instance of: scholarly article
title: Some problems in functional analysis inspired by Hahn-Banach type theorems
zbMATH Open document ID: 1317.46003
author: Mohd Amin Sofi
published in: Annals of Functional Analysis
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1310.3382
full work available at URL: AFA-tex v5 n2 a1.pdf
review text: This interesting survey paper deals with various aspects of the Hahn-Banach extension theorem for Banach spaces. Among the topics covered by the author are the following: applications of the Hahn-Banach theorem in analysis, Hahn-Banach type theorems for operators, uniqueness of the Hahn-Banach extension, the Hahn-Banach theorem for bilinear mappings, properties around the Hahn-Banach theorem characterising finite-dimensional spaces, characterisations of Hilbert spaces by Hahn-Banach type properties, intersection properties of balls, extension of Lipschitz maps. The author displays only few proofs, but points to the literature instead; the reference list, which contains a number of not so well-known papers, gives ample opportunity to pursue the subject matter further. The paper would have benefitted from proper proof-reading and copy-editing; there are mathematical ambiguities, language slips, misspelt names and typographical imperfections that could have been avoided.
reviewed by: Dirk Werner
Mathematics Subject Classification ID: 46-02
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46C15
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 6335713
zbMATH Keywords: Hahn-Banach extension theorem
zbMATH Keywords: injective Banach spaces
zbMATH Keywords: extension of Lipschitz maps
zbMATH Keywords: Hilbert-Schmidt spaces
zbMATH Keywords: intersection properties of balls
MaRDI profile type: Publication
OpenAlex ID: W1963750648
arXiv ID: 1310.3382
DOI: 10.15352/AFA/1396833499
description: scientific article; zbMATH DE number 6335713