Functional Analysis

Functional Analysis, Second Edition is an exposition of the theory of topological vector spaces, partially ordered spaces, and the development of the theory of integral operators and their representations on ideal spaces of measurable functions. Although this edition has deviated substantially from the first edition, it has still retained the overall plan, selection, and arrangement of the topics. The text is primarily devoted to the applications of functional analysis to applied analysis. However, these concepts have been extended and modernized. Some topics of functional analysis connected with applications to mathematical economics and control theory are also included in this edition. The applications of functional analysis are both wide and far-reaching as these are common language for all areas of mathematics involving the concept of continuity. Those who are in the field of mathematics, mechanics, and theoretical physics will find this book a valuable resource. Pt. I: Linear Operators And Functionals: Topological And Metric Spaces -- Vector Spaces -- Topological Vector Spaces -- Normed Spaces -- Linear Operators And Functionals -- The Analytical Representation Of Functionals -- Sequences Of Linear Operators -- The Weak Topology In A Banach Space -- Compact And Adjoint Operators -- Ordered Normed Spaces -- Integral Operators. Pt. Ii: Functional Equations: The Adjoint Equation -- Functional Equations Of The Second Kind -- A General Theory Of Approximation Methods -- The Method Of Steepest Descent -- The Fixed-point Principle -- Differentiation Of Non-linear Operators -- Newton's Method. By L. V. Kantorovich And G. P. Akilov ; Translated By Howard L. Silcock. Translation Of Funkt︠s︡ionalʹnyĭ Analiz. Includes Index. Bibliography: P. 571-576.