Hardcover ISBN:  9780883853573 
Product Code:  DOL/49 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614442134 
Product Code:  DOL/49.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853573 
eBook: ISBN:  9781614442134 
Product Code:  DOL/49.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 
Hardcover ISBN:  9780883853573 
Product Code:  DOL/49 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9781614442134 
Product Code:  DOL/49.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853573 
eBook ISBN:  9781614442134 
Product Code:  DOL/49.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 49; 2013; 137 pp
This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixedpoint theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

Table of Contents

Chapters

Chapter 1. Fundamentals

Chapter 2. Ode to the Dual Space

Chapter 3. Hilbert Space

Chapter 4. The Algebra of Operators

Chapter 5. Banach Algebra Basics

Chapter 6. Topological Vector Spaces

Chapter 7. Distributions

Chapter 8. Spectral Theory

Chapter 9. Convexity

Chapter 10. FixedPoint Theorems


Additional Material

Reviews

This book is a short introduction to functional analysis along with a brief description of the most well known examples. It opens with a chapter on the mathematical fundamentals and then moves on to the primary examples. It is written at a level where the practicing mathematician or upper level graduate student can use it as a standalone resource to learn the basics of functional analysis. Proofs of all of the main theorems and propositions are included. Krantz has won many awards for his skill at expository writing and with this book he once again demonstrates that he deserves all of the accolades he receives.
Charles Ashbacher, Journal of Recreational Mathematics 
This book (barely over 100 pages of text) is very short...but nevertheless addresses most or all of the standard topics that one would expect to see in an introductory graduatelevel semester in functional analysis, and perhaps even one or two things that might not get mentioned.
... Like other books in the Guide series, this one contains a good selection of examples, which I think is crucial. Another particularly nice feature of this book is the attention paid to applications of functional analysis, which even longer books frequently overlook. As some (nonexhaustive) examples, we see here, for example, the Uniform Boundedness theorem used to prove the existence of a broad class of functions with divergent Fourier series, the HahnBanach theorem invoked to establish the existence of the Green's function for smoothly bounded domains in the plane, and the contraction mapping principle used both to establish an existenceuniqueness theorem for differential equations and to give an elegant proof of the implicit function theorem.
... This book continues the tradition of highquality expositions that have characterized every other Guide that I have looked at. This series in general, and this book in particular, deserve, and I hope will get, a wide audience.
Mark Hunacek, MAA Reviews


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This book is a quick but precise and careful introduction to the subject of functional analysis. It covers the basic topics that can be found in a basic graduate analysis text. But it also covers more sophisticated topics such as spectral theory, convexity, and fixedpoint theorems. A special feature of the book is that it contains a great many examples and even some applications. It concludes with a statement and proof of Lomonosov's dramatic result about invariant subspaces.

Chapters

Chapter 1. Fundamentals

Chapter 2. Ode to the Dual Space

Chapter 3. Hilbert Space

Chapter 4. The Algebra of Operators

Chapter 5. Banach Algebra Basics

Chapter 6. Topological Vector Spaces

Chapter 7. Distributions

Chapter 8. Spectral Theory

Chapter 9. Convexity

Chapter 10. FixedPoint Theorems

This book is a short introduction to functional analysis along with a brief description of the most well known examples. It opens with a chapter on the mathematical fundamentals and then moves on to the primary examples. It is written at a level where the practicing mathematician or upper level graduate student can use it as a standalone resource to learn the basics of functional analysis. Proofs of all of the main theorems and propositions are included. Krantz has won many awards for his skill at expository writing and with this book he once again demonstrates that he deserves all of the accolades he receives.
Charles Ashbacher, Journal of Recreational Mathematics 
This book (barely over 100 pages of text) is very short...but nevertheless addresses most or all of the standard topics that one would expect to see in an introductory graduatelevel semester in functional analysis, and perhaps even one or two things that might not get mentioned.
... Like other books in the Guide series, this one contains a good selection of examples, which I think is crucial. Another particularly nice feature of this book is the attention paid to applications of functional analysis, which even longer books frequently overlook. As some (nonexhaustive) examples, we see here, for example, the Uniform Boundedness theorem used to prove the existence of a broad class of functions with divergent Fourier series, the HahnBanach theorem invoked to establish the existence of the Green's function for smoothly bounded domains in the plane, and the contraction mapping principle used both to establish an existenceuniqueness theorem for differential equations and to give an elegant proof of the implicit function theorem.
... This book continues the tradition of highquality expositions that have characterized every other Guide that I have looked at. This series in general, and this book in particular, deserve, and I hope will get, a wide audience.
Mark Hunacek, MAA Reviews