Linear Functional Analysis

Second Edition

Bryan P. Rynne and Martin A. Youngson

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.

The book contains a large number of exercises, with detailed solutions provided.

Further features of the second edition include:

• a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis;
• extended coverage of the uniform boundedness theorem;

Some background links

• Banach
• Hilbert
• Frechet
• Deficiencies of the Riemann Integral
• The origins of the abstract theory of linear spaces
• The origins of topology

Misprints

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:   .

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