A Guide to Functional Analysis.

cover -- copyright page -- title page -- Contents -- Preface -- Fundamentals -- What is Functional Analysis? -- Normed Linear Spaces -- Finite-Dimensional Spaces -- Linear Operators -- The Baire Category Theorem -- The Three Big Results -- Applications of the Big Three -- Ode to the Dual Space -- Introduction -- Consequences of the Hahn-Banach Theorem -- Hilbert Space -- Introduction -- The Geometry of Hilbert Space -- The Algebra of Operators -- Preliminaries -- The Algebra of Bounded Linear Operators -- Compact Operators -- Banach Algebra Basics -- Introduction to Banach Algebras -- The Structure of a Banach Algebra -- Ideals -- The Wiener Tauberian Theorem -- Topological Vector Spaces -- Basic Ideas -- Fréchet Spaces -- Distributions -- Preliminary Remarks -- What is a Distribution? -- Operations on Distributions -- Approximation of Distributions -- The Fourier Transform -- Spectral Theory -- Background -- The Main Result -- Convexity -- Introductory Thoughts -- Separation Theorems -- The Main Result -- Fixed-Point Theorems -- Banach's Theorem -- Two Applications -- The Schauder Theorem -- Table of Notation -- Glossary -- Bibliography -- Index -- About the Author.

This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixed-point theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.