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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
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

3 Answers 3

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

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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