Theory of Linear Operations

by Banach

• ISBN13: 9780444701848
• ISBN10: 0444701842
• Edition: 2nd
• Format: Hardcover
• Copyright: 1987-03-01
• Publisher: Elsevier Science

Summary

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a 1 x 1 + a 2 x 2 + ... + a n x n of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the p th -power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (''Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

Table of Contents

The Lebesgue-Stieltjes Integral

(B)-Measurable Sets and Operators in Metric Spaces

Groups

General Vector Spaces

F-Spaces

Normed Spaces

Banach Spaces

Compact Operators

Biorthogonal Sequences

Linear Functionals

Weakly Convergent Sequences

Linear Functional Equations

Isometry, Equivalence, Isomorphism

Linear Dimension

Appendix: Weak Convergence in Banach Spaces

Some Aspects of the Present Theory of Banach Spaces by A. Pelczynski and Cz. Bessaga

Reflexive and Weakly Compactly Generated Banach Spaces

Related Counter Examples

Local Properties of Banach Spaces

The Approximation Property and Bases

Characterizations of Hilbert Spaces in the Class of Banach Spaces

Classical Banach Spaces

The Topological Structure of Linear Metric Spaces

Bibliography

Table of Contents provided by Publisher. All Rights Reserved.