Heriot-Watt University

Linear Functional Analysis

Second Edition

Bryan P. Rynne and Martin A. Youngson

Published by Springer-Verlag, in the Springer Undergraduate Mathematics Series.
ISBN: 1-84800-004-9
First edition:   2000.     Second edition:   2008.

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material.

The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.

Further features of the second edition include:

Some background links

These links describe some of the early development of functional analysis, and also provide brief biographies of some of the people most closely associated with the subject (and, in the case of Banach and Hilbert, whose names have been given to the most important classes of spaces occurring in functional analysis).


Known misprints (other than obvious spelling and grammatical errors):

First Edition

Second Edition

The authors would be grateful to receive details of any misprints (for either edition), or any other constructive comments, which should be sent to:   .

This page was last updated on .

Bryan Rynne / Heriot-Watt University.   Email: