E-grāmata: Measure Theory And Functional Analysis

The focus of the graduate textbook is the interplay between topology, measure, and Hilbert space exhibited in the spectral theorem and its generalizations. Readers need to be familiar with metric spaces and abstract real and complex vector spaces. The objects of central importance all seem to be essentially countable in one way or another, he says, so whenever possible he assumes that topological spaces are metrizable, that measure spaces of sigma-finite, that Banach spaces are either separable or have separable preduals, and other matters to eliminate uncountable settings. His topics are topological spaces, measure and integration, Banach spaces, dual Banach spaces, and spectral theory. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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.