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• 

  Xenik

  星5つ中5つ

  Great textbook

  2023年8月23日にアメリカ合衆国でレビュー済み

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  I normally don't write that many reviews, but I had to go out of my way to write one. This textbook is god-tier. Definitely a slow and dense read, but that's not a bad thing. I have just finished chapter 2 going into Hilbert Spaces for my functional analysis class at Berkeley. If you're thinking about starting to read this textbook, I'd recommend learning metric spaces with limits and continuity beforehand since I felt some proofs assumed knowledge in these areas. It might be possible to translate all the topological theories into metric space ones, but he doesn't do that.

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  Jordan Bell

  星5つ中4つ

  Good exercises

  2015年8月22日にアメリカ合衆国でレビュー済み

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  Each section in this book introduces some object or property, proves a few theorems, and then has many exercises. These exercises are the best part of the book: there are many straightforward exercises that one needs to work through to become familiar with the objects you are working with, and even the harder exercises train the reader to use the objects they have been shown, rather than ask the reader to prove significant theorems. I first learned Banach spaces using this book, and the first three chapters are as good a place as any to learn locally convex spaces (which some functional analysis books unfortunately pass over, and then give ad-hoc explanations for the structure of the Schwartz space), Banach spaces, and Hilbert spaces. One especially nice result that is proved for Hilbert spaces is the polar decomposition, which is enormously useful when working with Hilbert-Schmidt and trace class operators and which is proved directly without using the spectral theorem.

  I don't like the chapter on Banach algebras as much as I do the first three chapters: for Banach algebras and the spectral theorem, I greatly prefer Rudin's Functional Analysis. The chapter on unbounded operators is not bad, although I still prefer Rudin, but Pedersen includes the Friedrichs extension, which Rudin doesn't cover. If this book is ever further revised for another edition (not by the author, who died in 2004), it would be helpful to make the ideas more concrete and because this is a big place the ideas are used to add a section on Sobolev spaces, to make explicit how they are the maximal domains of unbounded operators on the Hilbert space L^2.

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  ありがとうございます。数日中に調査いたします。

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• 

  SHAOSAI HUANG

  星5つ中5つ

  tough but rewarding reading

  2011年11月2日にアメリカ合衆国でレビュー済み

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  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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  ありがとうございます。数日中に調査いたします。

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  Thomas J. Bao

  星5つ中4つ

  Incredibly dense and concise; not for beginners

  2010年2月17日にアメリカ合衆国でレビュー済み

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  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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