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The book provides a detailed treatment of the essentials of Banach spaces, Hilbert spaces, Banach algebras, and locally convex spaces. The material developed here should prepare the reader for the study of a variety of topics in mathematics including differential equations, distribution theory, and abstract Fourier analysis, as well as areas in theoretical physics and the applied sciences.
The book assumes that the reader has an undergraduate background in real analysis and an acquaintance with basic linear algebra and properties of complex numbers. Metric spaces, general topology, and integration are developed in detail in the first two chapters.
The book should be of use to advanced undergraduates and first-year graduate students, and is also suitable for self-study. There are over 500 exercises to reinforce the material in the text, including exercises of independent interest. Hints are provided for the more difficult exercises, and complete solutions to selected problems are given in an appendix.
Hugo D. Junghenn is a Professor of Mathematics at The George Washington University. His research interests include functional analysis, semigroups, and probability.
He has published numerous journal articles and is the author of several books, Discrete Mathematics with Coding, CRC Press, 2023, An Introduction to Financial Mathematics, CRC Press, 2019 Principles of Analysis, CRC Press, 2018, including A Course in Real Analysis, CRC Press, 2015 and Options Valuation: A First Course in Financial Mathematics, CRC Press, 2011