Overview
- Tailored to novice mathematicians and non-specialists who wish to learn functional analysis with minimal prerequisites
- Contains many interesting examples and challenging exercises
- Covers a selection of topics that, while decades old, are of lasting value to both pure and applied mathematics
- Presents an outstanding treatment of Banach spaces and operator theory, being written by a specialist in these areas
Part of the book series: Universitext (UTX)
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Table of contents (11 chapters)
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Front Matter
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Topology
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Front Matter
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Measure Theory and Integration
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Front Matter
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Banach Spaces
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Front Matter
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Operator Theory
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Front Matter
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Back Matter
Keywords
About this book
This book provides a unique path for graduate or advanced undergraduate students to begin studying the rich subject of functional analysis with fewer prerequisites than is normally required. The text begins with a self-contained and highly efficient introduction to topology and measure theory, which focuses on the essential notions required for the study of functional analysis, and which are often buried within full-length overviews of the subjects. This is particularly useful for those in applied mathematics, engineering, or physics who need to have a firm grasp of functional analysis, but not necessarily some of the more abstruse aspects of topology and measure theory normally encountered. The reader is assumed to only have knowledge of basic real analysis, complex analysis, and algebra.
The latter part of the text provides an outstanding treatment of Banach space theory and operator theory, covering topics not usually found together in other books on functional analysis. Written in a clear, concise manner, and equipped with a rich array of interesting and important exercises and examples, this book can be read for an independent study, used as a text for a two-semester course, or as a self-contained reference for the researcher.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fundamentals of Functional Analysis
Authors: Douglas Farenick
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-45633-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-45631-7Published: 02 November 2016
eBook ISBN: 978-3-319-45633-1Published: 24 October 2016
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 451
Number of Illustrations: 2 b/w illustrations
Topics: Functional Analysis, Measure and Integration, Operator Theory