A Guide to Functional Analysis (Dolciani Mathematical Expositions 49)
By: Steven G. Krantz (author)Hardback
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Functional analysis is an abstract and powerful modern theory that occupies a central role in mathematics. This book provides a quick but precise introduction to the subject, covering everything that a beginning graduate student needs to know. The subject has its roots in the theory of infinite-dimensional vector spaces which is where the book begins, with preliminaries from the theory of normed linear spaces, Hilbert spaces, operator algebras and distributions. The reader will then encounter more advanced topics such as spectral theory, convexity and fixed-point theorems. It contains plenty of examples and exercises, making it an ideal basis for advanced undergraduate and graduate level courses in a subject that has become an essential part of every analyst's toolkit.
Steven G. Krantz earned a BA from the University of California, Santa Cruz and a PhD from Princeton University. He has taught at the University of California, Los Angeles, Pennsylvania State University, and Washington University. Over the course of his career he has written over 70 books and over 180 scholarly papers. He is a fellow of the American Mathematical Society and the holder of the Chauvenet Prize, the Beckenbach Book Award, and the UCLA Alumni Foundation Teaching Award.
Preface; 1. Fundamentals; 2. Ode to the dual space; 3. Hilbert space; 4. The algebra of operators; 5. Banach algebra basics; 6. Topological vector spaces; 7. Distributions; 8. Spectral theory; 9. Convexity; 10. Fixed-point theorems; Table of notation; Glossary; Bibliography; Index.
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- ID: 9780883853573
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