A guide to functional analysis / Steven G. Krantz, Washington University in St. Louis.

Format:

Book

Author/Creator:

Krantz, Steven G. (Steven George), 1951- author.

Series:

Dolciani Mathematical Expositions

Dolciani mathematical expositions ; no. 49

MAA guides ; no. 9

Dolciani Mathematical Expositions, v. 49

Language:

English

Subjects (All):

Functional analysis.

Physical Description:

1 online resource (xii, 137 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington : Mathematical Association of America, 2013.

Language Note:

English

Summary:

The purpose of A Guide to Functional Analysis is to introduce the reader with minimal background to the basic scripture of functional analysis. Readers should know some real analysis and some linear algebra. Measure theory rears its ugly head in some of the examples and also in the treatment of spectral theory. The latter is unavoidable and the former allows us to present a rich variety of examples. The nervous reader may safely skip any of the measure theory and still derive a lot from the rest of the book. Apart from this caveat, the book is almost completely self-contained; in a few instances we mention easily accessible references. A feature that sets this book apart from most other functional analysis texts is that it has a lot of examples and a lot of applications. This helps to make the material more concrete, and relates it to ideas that the reader has already seen. It also makes the book more accessible to a broader audience.

Contents:

Fundamentals

Ode to the dual space

Hilbert space

The algebra of operators

Banach algebra basics

Topological vector spaces

Distributions

Spectral theory

Convexity

Fixed-point theorems.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-61444-213-4

OCLC:

939263618