Theory of Linear Operations

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.Banach, Stefan is the author of 'Theory of Linear Operations' with ISBN 9780444701848 and ISBN 0444701842.