Hilbert Spaces: A Brief Historical Introduction

Abstract

This introduction explains very briefly how and why the theory of Hilbert spaces and their operators emerged. In particular we mention which type of mathematical problems motivated the emergence of these spaces at the beginning of the 20th century as a generalization of finite linear vector spaces that have an inner product and therefore also metric and geometric properties. Then we present a short overview of the contents of this second part on Hilbert spaces and their operators. The final part of this introduction contains remarks on the particular and fundamental rôle which quantum physics has played in the development of the theory of Hilbert spaces and of modern functional analysis.