The establishment of functional analysis
type: Item
instance of: scholarly article
title: The establishment of functional analysis
zbMATH Open document ID: 0549.01001
DOI: 10.1016/0315-0860(84)90036-3
author: Erwin O. Kreyszig
author: Garrett. Birkhoff
published in: Historia Mathematica
publication date: 1984-01-01T00:00:00Z
review text: This comprehensive survey of functional analysis treats its sources and development up to the publication of Banach's book. Once reasonably clear notions of function and space were in place, the basic ideas were developed first by Italian and slightly later by French investigators. Calculus of variations and integral equations provided the occasion to hone and apply the tools of abstract analysis. The work of Hilbert and his associates as well as of Frédéric Riesz is discussed in detail. A brief survey of early point set topology leads into an account of Banach's work and the fundamental theorems of functional analysis. The paper concludes with a discussion of papers delivered at Bologna in 1928, research into fixed point and ergodic theory and the contributions of von Neumann and M. H. Stone.
Mathematics Subject Classification ID: 01A05
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 46-03
zbMATH DE Number: 3875196
zbMATH Keywords: Calculus of variations
zbMATH Keywords: integral equations
zbMATH Keywords: abstract analysis
zbMATH Keywords: Hilbert
zbMATH Keywords: Frédéric Riesz
zbMATH Keywords: point set topology
zbMATH Keywords: Banach
zbMATH Keywords: von Neumann
zbMATH Keywords: M. H. Stone
reviewed by: Edward J. Barbeau
MaRDI profile type: Publication
full work available at URL: 0315-0860(84)90036-3
OpenAlex ID: W2083372415
cites work: Q5183447
cites work: Q5802100
cites work: Q4044490
cites work: Q4090273
cites work: Q3935670
cites work: Q3803064
cites work: Q3254057
cites work: Q4146094
cites work: Q5683241
cites work: Q5581566
cites work: Q5830633
cites work: Q4334625
cites work: A study of Maurice Frechet. I: His early work on point set theory and the theory of functionals
cites work: Q5549011
cites work: Q4106143
description: scientific article; zbMATH DE number 3875196