A course in abstract analysis
著者
書誌事項
A course in abstract analysis
（Graduate studies in mathematics, v. 141）
American Mathematical Society, c2012
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注記
Includes bibliographical references (p. 359-360) and index
内容説明・目次
内容説明
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single variable and the elements of metric spaces. Following the author's belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
目次
Preface
Chapter 1. Setting the stage
Chapter 2. Elements of measure theory
Chapter 3. A Hilbert space interlude
Chapter 4. A return to measure theory
Chapter 5. Linear transformations
Chapter 6. Banach spaces
Chapter 7. Locally convex spaces
Chapter 8. Duality
Chapter 9. Operators on a Banach space
Chapter 10. Banach algebras and spectral theory
Chapter 11. C*-algebras
Appendix
Bibliography
List of symbols
Index
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