An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras
2014, XI, 420 p. 75 illus.
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Provides a self-contained introduction to functional analysis, assuming only real analysis and linear algebra
Presents the essential aspects of metric spaces, Hilbert spaces, Banach spaces and Banach algebras
Includes interesting applications of Hilbert spaces such as least squares approximation and inverse problems
Prepares the reader for graduate-level mathematical analysis
This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.
Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.
Content Level »Upper undergraduate
Keywords »Banach Algebra - Banach Space - Functional Analysis - Hilbert Space - Metric Space