Functional Analysis

Functional Analysis examines trends in functional analysis as a mathematical discipline and the ever-increasing role played by its techniques in applications. The theory of topological vector spaces is emphasized, along with the applications of functional analysis to applied analysis. Some topics of functional analysis connected with applications to mathematical economics and control theory are also discussed. Comprised of 18 chapters, this book begins with an introduction to the elements of the theory of topological spaces, the theory of metric spaces, and the theory of abstract measure spaces. Many results are stated without proofs. The discussion then turns to vector spaces, normed spaces, and linear operators and functionals. Subsequent chapters deal with the analytic representation of functionals; sequences of linear operators; the weak topology in a Banach space; and compact and adjoint operators. The last section focuses on functional equations, including the adjoint equation and functional equations of the second kind. This monograph is intended for students specializing in mathematical analysis and computational mathematics.