Springer Undergraduate Mathematics Series

Linear Functional Analysis

Authors: Rynne, Bryan, Youngson, M.A.

  • A new chapter on the Hahn-Banach theorem and extended material of the uniform boundedness theorem complete the coverage and make the book even more suitable for an introductory course on functional analysis
  • Detailed explanations and proofs and plenty of exercises - with full solutions provided at the back of the book - make this book ideal for reading courses and for self-study
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4471-3655-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this Textbook

This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material.

The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.

Further highlights of the second edition include:

a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis;

extended coverage of the uniform boundedness theorem;

plenty of exercises, with solutions provided at the back of the book.

Praise for the first edition:

"The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having 'gotten somewhere worth getting' by a sensibly paced, clearly signposted route." Mathematical Gazette

"It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE

Reviews

From the reviews of the second edition:

"The authors write with a strong narrative thrust and a sensitive appreciation of the needs of the average student so that, by the final chapter, there is a real feeling of having "gotten somewhere worth getting" by a sensibly paced, clearly signposted route." Mathematical Gazette, 2000

"It is a fine book, with material well-organized and well-presented. A particularly useful feature is the material on compact operators and applications to differential equations." CHOICE magazine

"The presentation is quite elementary, and there are sufficiently many illuminating examples and exercises… this nice textbook perfectly fits the readership, i.e., undergraduate students in mathematics and physics… It may be recommended to all students who want to get in touch with the basic ideas of functional analysis and operator theory for the first time." Zentralblatt MATH

"This is an undergraduate introduction to functional analysis, with minimal prerequisites, namely linear algebra and some real analysis. … It is extensively cross-referenced, has a good index, a separate index of symbols (Very Good Feature), and complete solutions to all the exercises. It has numerous examples, and is especially good in giving both examples of objects that have a given property and objects that do not have the property." (Allen Stenger, MathDL, April, 2008)

"This second revised edition of the book … covers the normed aspects in functional analysis and consists of the preface, eight chapters, solutions to exercises (at the end of the book), a bibliography containing 17 references, notation index and subject index. … The book is readable and conceptually useful for undergraduate students in mathematics and physics. The authors show well how essential concepts from finite-dimensional linear algebra can be extended to the infinite-dimensional case." (Mohammad Sal Moslehian, Zentralblatt MATH, Vol. 1144, 2008)


Table of contents (8 chapters)

  • Preliminaries

    Rynne, Bryan Patrick (et al.)

    Pages 1-30

  • Normed Spaces

    Rynne, Bryan Patrick (et al.)

    Pages 31-50

  • Inner Product Spaces, Hilbert Spaces

    Rynne, Bryan Patrick (et al.)

    Pages 51-85

  • Linear Operators

    Rynne, Bryan Patrick (et al.)

    Pages 87-121

  • Linear Operators on Hilbert Spaces

    Rynne, Bryan Patrick (et al.)

    Pages 123-160

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4471-3655-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Linear Functional Analysis
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2000
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London
eBook ISBN
978-1-4471-3655-2
DOI
10.1007/978-1-4471-3655-2
Series ISSN
1615-2085
Edition Number
1
Number of Pages
X, 273
Topics