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 a1x1 + a2x2 + .

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+ anxn 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.