Functional Analysis and Infinite-Dimensional Geometry / Edition 1

Hardcover (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $34.65
Usually ships in 1-2 business days
(Save 65%)
Other sellers (Hardcover)
  • All (14) from $34.65   
  • New (9) from $34.65   
  • Used (5) from $52.27   


This book introduces the basic principles of functional analysis and areas of Banach space theory that are close to nonlinear analysis and topology. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints.

Read More Show Less

Editorial Reviews

From the Publisher
From the reviews:

"This is a substantial text containing up-to-date exposition and functional analysis from a Banach space point of view. It will be particularly useful for research investigation of nonlinear functional analysis and optimization…This book will stand as an important working text and reference and a significant guide for research students." (Mathematical Reviews)

"This book can be warmly recommended to everyone interested in functional analysis, and Banach space theory in particular. It serves also as a textbook in courses for students in probability, physics, or engineering. Graduate students and researchers surely will find a lot of material from the field, as well as a source of inspiration." (European Mathematical Society Newsletter, September, 2003)

"This is a substantial text containing an up-to-date exposition of functional analysis … . It will be particularly useful for research investigation of nonlinear functional analysis and optimization. … Each chapter ends with a remarkably weighty collection of exercises, many of which have useful hints at solutions appended to them … . the reader is directed throughout to the ample collection of references. The book will stand as an important working text and reference and a significant guide for research students." (John R. Giles, Mathematical Reviews, Issue 2002 f)

"The sextet of authors have done a superb job in marshalling and presenting their material: the writing is crisp and authoritative and they take full advantage of recent simplifications in the proofs of certain results. The fulsome, up-to-date bibliography is accompanied by a marvellous collection of nearly 700 exercises (with integrated hints): for both learners and lecturers, this rich source of material alone is worth more than the cost of the book. … I warmly commend this book … ." (Nick Lord, The Mathematical Gazette, Vol. 87 (509), 2003)

"This book, which contains a vast amount of material, is intended as an introduction to linear function analysis … . At the end of each chapter there is a wealth of beautiful applications and exercises … . I would highly recommend this book to anyone interested in the study of Banach spaces … . I think it would be fair to say that if one knew half of the material contained in this book, then one would know quite a lot." (Warren Moors, The Australian Mathematical Society Gazette, Vol. 29 (5), 2002)

"This book is based on graduate courses taught at the university of Alberta in Edmonton. It is intended as an introduction to linear functional analysis and to some parts of infinite-dimensional Banach space theory. It is full of facts, theorems, corollaries; along with a large number of exercises with detailed hints for their solution. … The authors have accomplished a text which is easily readable and as self-contained as possible. A very excellent book for the topics covered." (Joe Howard, Zentralblatt MATH, Vol. 981, 2002)

"By its organization, the book can be used as a textbook for various types of courses in functional analysis … . Besides classical material, the book contains also some recent and more specialized results … . The book contains a large number of exercises with detailed hints, completing the main text with many important results. The book is a valuable contribution to Banach space literature and can be used as a solid introduction to functional analysis … ." (Stefan Cobzas, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLVII (2), 2002)

"The present book is … intended as an introduction to linear functional analysis … . Each chapter concludes with a separate section in which together nearly 700 exercises are listed. Almost all of them, as it seems, are supplemented with hints to their solution. The exercises are an important part of the general text, contain many important results and essentially complement the material in the chapters. … Altogether, the material presented is simply enormous and could fill with enthusiasm … ." (J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen, Vol. 20 (4), 2001)

Read More Show Less

Product Details

  • ISBN-13: 9780387952192
  • Publisher: Springer New York
  • Publication date: 5/25/2001
  • Series: CMS Books in Mathematics Series
  • Edition description: 2001
  • Edition number: 1
  • Pages: 451
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.00 (d)

Table of Contents

• 1 Basic Concepts in Banach Spaces
• 2 Hahn-Banach and Banach Open Mapping Theorems
• 3 Weak Topologies
• 4 Locally Convex Spaces
• 5 Structure of Banach Spaces
• 6 Schauder Bases
• 7 Compact Operators on Banach Spaces
• 8 Differentiability of Norms
• 9 Uniform Convexity
• 10 Smoothness and Structure
• 11 Weakly Compactly Generated Spaces
• 12 Topics in Weak Toplogy
• References
• Index

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)