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Elementary functional analysis

Author: Barbara D MacCluer
Publisher: New York : Springer, ©2009.
Series: Graduate texts in mathematics, 253.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"This text is intended for a one-semester introductory course in functional analysis for graduate students and well-prepared advanced undergraduates in mathematics and related fields. It is also suitable for self-study, and could be used for an independent reading course for undergraduates preparing to start graduate school." "While this book is relatively short, the author has not sacrificed detail. Arguments are  Read more...
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Genre/Form: Lehrbuch
Electronic books
Additional Physical Format: Print version:
MacCluer, Barbara D.
Elementary functional analysis.
New York : Springer, ©2009
(DLC) 2008937759
(OCoLC)258078575
Online version:
MacCluer, Barbara D.
Elementary functional analysis.
New York : Springer, ©2009
(OCoLC)812615472
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Barbara D MacCluer
ISBN: 9780387855295 0387855297
OCLC Number: 723099152
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL
Description: 1 online resource (x, 207 pages) : illustrations.
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: 1. Hilbert Space Preliminaries --
1.1. Normed Linear Spaces --
1.2. Orthogonality --
1.3. Hilbert Space Geometry --
1.4. Linear Functionals --
1.5. Orthonormal Bases --
1.6. Exercises --
2. Operator Theory Basics --
2.1. Bounded Linear Operators --
2.2. Adjoints of Hilbert Space Operators --
2.3. Adjoints of Banach Space Operators --
2.4. Exercises --
3. The Big Three --
3.1. The Hahn-Banach Theorem --
3.2. Principle of Uniform Boundedness --
3.3. Open Mapping and Closed Graph Theorems --
3.4. Quotient Spaces --
3.5. Banach and the Scottish Cafe --
3.6. Exercises --
4. Compact Operators --
4.1. Finite-Dimensional Spaces --
4.2. Compact Operators --
4.3. A Preliminary Spectral Theorem --
4.4. The Invariant Subspace Problem --
4.5. Introduction to the Spectrum --
4.6. The Fredholm Alternative --
4.7. Exercises --
5. Banach and C*-Algebras --
5.1. First Examples --
5.2. Results on Spectra --
5.3. Ideals and Homomorphisms --
5.4. Commutative Banach Algebras --
5.5. Weak Topologies --
5.6. The Gelfand Transform --
5.7. The Continuous Functional Calculus --
5.8. Fredholm Operators --
5.9. Exercises --
6. The Spectral Theorem --
6.1. Normal Operators Are Multiplication Operators --
6.2. Spectral Measures --
6.3. Exercises --
Appendix A. Real Analysis Topics --
A.1. Measures --
A.2. Integration --
A.3. L[superscript p] Spaces --
A.4. The Stone-Weierstrass Theorem --
A.5. Positive Linear Functionals on C(X).
Series Title: Graduate texts in mathematics, 253.
Responsibility: Barbara D. MacCluer.

Abstract:

This concise text on functional analysis is gently written and covers a unique set of topics. It includes numerous high-quality exercises and interesting historical tidbits scattered throughout.  Read more...

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From the reviews: A review from Michael Berg, MAA Online:Barbara D. MacCluer's compact text, Elementary Functional Analysis, is an unusual book on a number of counts. For one, it unmistakably conveys Read more...

 
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