عنوان

Metrics, norms, inner products, and operator theory /

(Number (ISBN

3319653229

(Number (ISBN

9783319653228

Erroneous ISBN

3319653210

Erroneous ISBN

9783319653211

Title Proper

Metrics, norms, inner products, and operator theory /

General Material Designation

[Book]

First Statement of Responsibility

Christopher Heil.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Birkhäuser,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xxi, 359 pages) :

Other Physical Details

illustrations.

Series Title

Applied and numerical harmonic analysis,

ISSN of Series

2296-5009

Text of Note

Includes bibliographical references and index.

Text of Note

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.

0

Text of Note

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 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 (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.--

International Standard Book Number

3319653210

Banach spaces.

Mathematical analysis.

Operator theory.

Functional Analysis.

Operator Theory.

Banach spaces.

Mathematical analysis.

Operator theory.

Number

Edition

Class number

Heil, Christopher,1960-

Date of Transaction

20200823102244.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y