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Analysis Now (Graduate Texts in Mathematics) Hardcover – November 14, 2001

ISBN-13: 978-0387967882 ISBN-10: 0387967885 Edition: Corrected

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Editorial Reviews

Review

G.K. Pedersen

Analysis Now

"The writing is clear and precise, but has an informal and humorous touch which enlivens the material. One of the strengths of the book is the excellent set of problems, which accompany the text."—MATHEMATICAL REVIEWS

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Product Details

  • Series: Graduate Texts in Mathematics (Book 118)
  • Hardcover: 280 pages
  • Publisher: Springer; Corrected edition (November 14, 2001)
  • Language: English
  • ISBN-10: 0387967885
  • ISBN-13: 978-0387967882
  • Product Dimensions: 6.1 x 0.8 x 9.2 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #1,584,735 in Books (See Top 100 in Books)

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Customer Reviews

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Most Helpful Customer Reviews

14 of 14 people found the following review helpful By Sheeyun Park on April 3, 2000
Format: Hardcover
A brisk tour through modern functional analysis. Covers the 'foundational' topics such as the Hahn-Banach Thm, the Baire Category Thm, the Krein-Millman Thm, and the Spectral Thm for bounded and unbounded operators. Also includes expositions on Gelfand Transforms, maximal commutative algebras, and trace class operators. Ends with a chapter on measure and integration theory from the functional analysis point of view.
Pretty dense exposition but very clear and well organized. Lots of challenging excercises. I wouldn't recommend it as a first introduction to functional analysis unless the reader has a strong background in analysis and topology. However, I would recommend it as a good reference or second text on functional analysis. The author also periodically injects enjoyable short anecdotes.
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9 of 9 people found the following review helpful By Bernardo Vargas on April 1, 2000
Format: Hardcover
Originally conceived as a quick introduction to modern operator theory, this book surveys from the very foundations of analysis (topological sapaces, normed spaces, etc.) up to a state-of-the-art exposition of integration theory, stepping through spectral theory, unbounded operators, and more.
Its style is adequately abstract, rigorous and concise. Covers more material than most of the old-fashioned classical references on the subject.
A must-reading for the graduate student. Even undregrads will find most parts acquaintable and useful.
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11 of 12 people found the following review helpful By Adrian Jenkins on April 23, 2012
Format: Hardcover
...but perhaps useful as a reference. Even then, I would caution the buyer to beware.

I chose this book for a course I gave at Iowa State on functional analysis, meant for students after a year of graduate analysis. The book was referred to me by another professor, although the recommendation wasn't glowing. All in all, the book has its pros and cons, although I would never recommend it for students. I wish I had spent more time perusing the proofs of the book.

My first caution is that one should be VERY careful and make sure you get the REPRINTED version of the book. If you are buying this used, be extra cautious. The original version is rife with errors (in both the development of the theory, as well as the numerous exercises present), some of them severe. This problem is worsened by the author's lack of detail in many of his proofs. Even if your only goal is to read theorems, without bothering with proofs, you will find multiple mistakes (for example, his statement of the Krein-Smulian is simply incorrect, and his proof has a clear gap, although it does work for the correct statement of the theorem). Caveat emptor.

The biggest pro of the book is the thorough nature of development of the theory. Although the proofs leave much to be desired, the first 2.5 chapters gives an excellent amount of material for the book, with a pretty full accounting of the theory of Banach Spaces (and even more general topological vector spaces, although the absence of Frechet spaces is troubling). The theory of strong, weak, and weak* topology is particularly nice - in a rare instance, the author is careful to give nice proofs, particularly when considering bases and subbases of the weak* topology.

However, there are issues here.
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2 of 2 people found the following review helpful By SHAOSAI HUANG on November 1, 2011
Format: Hardcover Verified Purchase
I used it as my introductory textbook to functional analysis. At the beginning I thought the prof was crazy. Indeed as a beginner it was a tough experience to learn from this book. I could still remember that I spend hours and hours checking his statements on weak and weak star topology in section 2.4 line by line... At the time I got really unhappy reading that book and complained a lot about it: its lack of intuitive explanation, its high density, its dry exercises... anything. But about 3 years after that reading, today I still benefit so much from that book. Whenever in studying PDE or probability, or operator algebras, hints and feelings suddenly jump out of that book from time to time. And finally I could see that the neat style of this book really gave me a good overall feeling on the subject; and the hard work of checking details left to the reader educates me a good habit of learning mathematics.
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2 of 4 people found the following review helpful By Thomas J. Bao on February 16, 2010
Format: Hardcover Verified Purchase
Functional Analysis was the first course in mathematics where I truly struggled everyday. Although I was fairly comfortable with banach spaces after taking measure theory, I had a brutally difficult time digesting weak topologies and an even harder one understanding hilbert spaces. I would really recommend that undergrads take an introduction course to functional analysis before trying this text.
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