Metrics, Norms, Inner Products, and Operator Theory. 1st ed. 2018

種類:

電子ブック

責任表示:

by Christopher Heil

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018

著者名:

• Heil, Christopher.
• SpringerLink (Online service)

シリーズ名:

Applied and Numerical Harmonic Analysis ;

ISBN:

9783319653228 [3319653229]    

注記:

Preface -- Notation and Preliminaries -- Metric Spaces -- Norms and Banach Spaces -- Further Results on Banach Spaces -- Inner Products and Hilbert Spaces -- Operator Theory -- Operators and Hilbert Spaces.
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 ℓp 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 undergrad

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