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Analysis Now (Graduate Texts in Mathematics) Corrected Edition

4.2 out of 5 stars 6 customer reviews
ISBN-13: 978-0387967882
ISBN-10: 0387967885
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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 (6 customer reviews)
  • Amazon Best Sellers Rank: #871,570 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

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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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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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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