Metrics, Norms, Inner Products, and Operator Theory

by Heil

This text is a self-contained introduction to the three main families that we encounter in analysis –  metric spaces, normed spaces , and  inner product spaces  – and to the operators that transform objects in one into objects in another.  With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of ℓ p  topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle.  The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style,  Metrics, Norms, Inner Products, and Operator Theory  is suitable for independent study or as the basis for an undergraduate-level course.  Instructors have several options for building a course around the text depending on the level and interests of their students. Key Unique text providing an undergraduate-level introduction to metrics, norms, inner products,  and  their associated operator theory. 

Genres: Mathematics

384 pages, Hardcover

Published September 11, 2018