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I'm studying functional analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) The books I'm searching for should be:

  • full of hard, non-obvious, non-common, and thought-provoking problems;
  • rich of complete, step by step, rigorous, and enlightening solutions;
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    $\begingroup$ Wojtaszczyk's text Banach Spaces for Analysts has nice hints provided for its nice problem sets. IMO, at this stage, you're beyond the point where full solutions will help. You could of course read a theorem in a text and attempt your own proof before looking at the provided proof. $\endgroup$ – David Mitra Sep 28 '14 at 10:00
  • $\begingroup$ Theorems and Problems in Functional Analysis by Kirillov and Gvishiani $\endgroup$ – Orest Bucicovschi Sep 28 '14 at 10:00
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Just to state my opinion: when you get to study functional analysis it is almost certainly that you are going into research, one way or another. At such level, "rich of complete, step by step, rigorous, and enlightening solutions" is probably not a good idea. When doing research, you won't find "complete, step by step, rigorous, and enlightening solutions" (if you do, it means that the research you did was already done by somebody else).

In all, when you are ready to take functional analysis you should be able to tell whether the solutions you found are correct. And if you can't, you always have math.stackexchange.

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I think you'll also enjoy A Hilbert Space Problem Book by Paul Halmos. The Preface of this book is interesting, and the book is written in the Halmos style. Not much else needs to be said.

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Try A A Kirillov, A D Gvishiani: Theorems and Problems in Functional Analysis.

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