Linear Analysis: An Introductory Course (Cambridge Mathematical Textbooks) [Paperback]

Béla Bollobás (Author)

Book Description

ISBN-10: 0521655773 | ISBN-13: 978-0521655774 | Publication Date: March 28, 1999 | Edition: 2

Now revised and updated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include the geometry of finite-dimensional spaces, invariant subspaces, fixed-point theorems, and the Bishop-Phelps theorem. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.

Editorial Reviews

Review

"The presentation is self-contained and lively and its outstanding feature is its brevity." Mathematical Reviews

Book Description

Now revised and up-dated, this brisk introduction to functional analysis is intended for advanced undergraduate students, typically final year, who have had some background in real analysis. The author's aim is not just to cover the standard material in a standard way, but to present results of application in contemporary mathematics and to show the relevance of functional analysis to other areas. An outstanding feature is the large number of exercises, some straightforward, some challenging, none uninteresting.

Product Details

• Paperback: 256 pages
• Publisher: Cambridge University Press; 2 edition (March 28, 1999)
• Language: English
• ISBN-10: 0521655773
• ISBN-13: 978-0521655774
• Product Dimensions: 9 x 6 x 0.6 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,485,183 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

4 of 5 people found the following review helpful:

4.0 out of 5 stars Five stars for content; two stars for printing, June 6, 2008

By 

Christopher Grant (Salem, UT USA) - See all my reviews
(REAL NAME)   

This review is from: Linear Analysis: An Introductory Course (Cambridge Mathematical Textbooks) (Paperback)

I'm a math professor in the middle of developing an introductory functional analysis course whose prerequisites will be elementary linear algebra and metric space theory and whose intended focus will be on the *abstract* theory of normed spaces and bounded linear operators between them. This book by Bollobas is about the best fit for the class that I've been able to find after an extensive search. The author covers about the right topics in about right the depth, and from what I've been able to tell it is well-organized and well-written.

During the development of this curriculum, I've been using a 1999 printing of this book borrowed from the library, and it impressed me enough that I ordered a copy of my own from Amazon, which arrived just this afternoon. To my dismay, I learned that this book, like so many of Cambridge University Press's older works, has fallen victim to the "digital printing" scourge. Contrary to what Amazon's "Search Inside!" feature indicates, the copyright page now reads "Transferred to digital printing 2004". Not that you need the copyright page to tell you that, because the loss of crispness in the typography makes that abundantly clear. And, of course, this new copy has a "perfect binding" (a misnomer if ever there was one). If you like a book with a nice professional look to it, don't get your hopes up with this one. What a shame.

2 of 5 people found the following review helpful:

3.0 out of 5 stars Good writing, OK coverage, October 27, 2005

By 

Nathan Oakes (Ashland, Oregon) - See all my reviews

This review is from: Linear Analysis: An Introductory Course (Cambridge Mathematical Textbooks) (Paperback)

This undergrad text is very clear and Bollobas has a friendly style of writing. The coverage, though, is rather narrow and there are no applications. So I like Kreyszig better.