Characterizations of inner product spaces
type: Item
instance of: scholarly article
title: Characterizations of inner product spaces
zbMATH Open document ID: 0617.46030
author: Dan Amir
published in: Operator Theory: Advances and Applications
publication date: 1986-01-01T00:00:00Z
review text: This is an excellent, selfcontained, up-to-date, exhaustive survey on various isometric characterizations of inner product spaces. In Chapter 2 on 2-dimensional characterizations the author discusses among others James and Birkhoff orthogonality characterizations as well as norm derivatives and best approximation characterizations. In Chapter 3 on 3-dimensional characterizations the characterizations included range from classical Kakutani's result, through metric projections characterizations to Chebyshev centers and proximinal maximal subspaces, to name just a few topics covered in the book. The book is well written, well organized. It bears a seal of expertize of the author who is a renowned specialist in the theory of normed spaces. The book will certainly be a useful source for researchers both in this area as well as in many related areas of functional analysis, geometry and approximation theory.
Mathematics Subject Classification ID: 46C05
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46-02
zbMATH DE Number: 4000736
zbMATH Keywords: isometric characterizations of inner product spaces
zbMATH Keywords: James and Birkhoff orthogonality
zbMATH Keywords: norm derivatives
zbMATH Keywords: best approximation
zbMATH Keywords: Chebyshev centers
zbMATH Keywords: proximinal maximal subspaces
reviewed by: V. Zizler
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4000736