This clear and concise text provides a complete survey of the basic theory of Banach spaces, Hilbert spaces, and linear transformations, including the self-adjoint type, as well as commutative Banach algebras with a unit. Author Edgar R. Lorch was a leader in the development of modern mathematics theory, and this volume encompasses some of his contributions to the field of spectral theory, including his theory of reducibility of operators. Suitable for advanced undergraduate and graduate students, this treatment forms a solid foundation for future courses in real and complex variables. Prerequisites include set theory, metric spaces, and abstract algebra. Exercises appear throughout the book, including at chapter ends, where they highlight informal discussions of examples. The text is also of particular interest to engineers and physicists seeking insights into the abstract theory that underlies differential and integral operators.
