Metrics, Norms, Inner Products, and Operat...

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Beschreibung

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 ¿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 features:Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter.
Suitable for undergraduate-level courses; no familiarity with measure theory is required.
Extensive exercises complement the text and provide opportunities for learning by doing.
A separate solutions manual is available for instructors via the Birkhäuser website ([...]

Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

Über den Autor

Christopher Heil, Professor and Associate Chair, School of Mathematics, Georgia Institute of Technology

Zusammenfassung

Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter
Suitable for undergraduate-level courses; no familiarity with measure theory is required
Extensive exercises complement the text and provide opportunities for learning by doing
A separate solutions manual is available for instructors via the Birkhäuser website ([...]
Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Applied and Numerical Harmonic Analysis
Inhalt:	xxi 359 S. 35 s/w Illustr. 359 p. 35 illus.
ISBN-13:	9783030097370
ISBN-10:	3030097374
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Heil, Christopher
Auflage:	Softcover reprint of the original 1st ed. 2018
Hersteller:	Springer International Publishing Springer International Publishing AG Applied and Numerical Harmonic Analysis
Maße:	235 x 155 x 21 mm
Von/Mit:	Christopher Heil
Erscheinungsdatum:	15.12.2018
Gewicht:	0,581 kg