This ebook is a self-contained introduction to the three main families that we face in analysis – normed spaces, metric spaces, and inner product spaces– and to the operators that change objects in one into objects in another. With a focus on the fundamental properties defining the spaces, this ebook guides readers to a deeper understanding of analysis and an understanding of the field as the “science of functions.”
Many crucial topics that are hardly presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, the dual of ℓp topological isomorphisms, the Baire Category Theorem, Schauder bases for Banach spaces, the Spectral Theorem, and the Uniform Boundedness Principle. The text is designed in such a way that instructors have the option of whether to include more advanced topics.
Written in an accessible and appealing style, Metrics, Norms, Inner Products, and Operator Theory, (PDF) is suitable for independent study or as the foundation for an undergraduate-level course. Instructors have numerous options for building a course around the textbook depending on the interests and level of their students.
- Suitable for undergraduate-level courses; no knowledge of measure theory is required.
- Extensive exercises complement the ebook and provide opportunities for learning by doing.
- A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1).
- Aimed at students who have a fundamental knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter.
Unique textbook providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.
978-3030097370, 978-3319653211, 978-3030097370, 978-3319653228
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