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There are many excellent problem books in real analysis. I'm looking for a problem book in functional analysis or a book which contains a lot of problems in functional analysis (Easy and hard problems) to which a complete solution manual is readily available .

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I thought that Halmos' "A Hilbert Space Problem Book" was quite nice. I believe it also has a section with hints and then another one with more or less full solutions. –  brom Dec 12 '12 at 13:18
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You might want to have a look at Textbook of Functional Analysis: A Problem-oriented Approach by V. K. Krishnan. You might also want to review some of the recommendation here: math.stackexchange.com/questions/7512/… –  Amzoti Dec 12 '12 at 13:48
    
Simply searching in Google Books for exercises functional analysis or problems functional analysis might provide you some suggestions. (Of course, you will have judge for yourself which of them seem reasonable.) –  Martin Sleziak May 24 at 5:39

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A $C_p$-Theory Problem Book: Topological and Function Spaces by Vladimir V. Tkachuk (2011). (I think all problems are solved in the main book.)

Also, this link at mathoverflow.net might be helpful.

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Thanks for your recommendations . I think it's a very good book ,but I'm interested in a more applied point of view that's applicable to physics . Also ,at a first glance that book doesn't cover operator theory on hilbert space. –  physicsStudent Dec 13 '12 at 7:51
    
It is true that Tkachuk's book has solutions to all problems given there. And it seems to be a very good book, as far as I can say. However, I would classify it general topology rather than functional analysis. –  Martin Sleziak May 24 at 7:36

Theorems and Problems in Functional Analysis has a lot of problems with hints and solutions.

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this book is hard –  ILoveMath Nov 11 '13 at 1:03

Bernard Gelbaum's Problems in Real and Complex Analysis has a chapter on topological vector spaces, which are functional analysis problems.

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The book Fabian, Habala, Hájek, Montesinos, Zizler: Banach Space Theory, The Basis for Linear and Nonlinear Analysis (CMS Books in Mathematics) has many exercises at the end of each chapter. It does not have solutions, but most of the exercises come with some hint (in some cases rather detailed). Google Books link, DOI: 10.1007/978-1-4419-7515-7

This book was also recommended in some other posts on this site:

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