This book provides an introduction to measure theory and functional analysis suitable for a beginning graduate course, and is based on notes the author had developed over several years of teaching such a course. It is unique in placing special emphasis on the separable setting, which allows for a simultaneously more detailed and more elementary exposition, and for its rapid progression into advanced topics in the spectral theory of families of self-adjoint operators. The author's notion of measurable Hilbert bundles is used to give the spectral theorem a particularly elegant formulation not to be found in other textbooks on the subject.
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Contents:- Topological Spaces
- Measure and Integration
- Banach Spaces
- Dual Banach Spaces
- Spectral Theory
Readership: Graduates students in mathematics (pure and applied) in their first or second year, graduate students in physics or engineering, and economics.
Key Features:- A very readable and thorough treatment of the core material in measure theory and functional analysis which cuts a clear path to advanced results in the spectral theory of families of commuting self-adjoint operators, avoiding side topics of lesser importance
- Presents the author's elegant formulation of the spectral theorem in terms of his notion of Hilbert bundles, not available in comparable textbooks
- Uniquely firm emphasis on the separable case allows for a simultaneously more detailed and more elementary exposition
- Includes over 150 exercises
