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 .
problem books in functional analysis
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0Simply searching in Google Books for [exercises functional analysis](http://books.google.com/books?q=exercises+functional+analysis) or [problems functional analysis](http://books.google.com/books?q=problems+functional+analysis) might provide you some suggestions. (Of course, you will have judge for yourself which of them seem reasonable.) – 2019-05-06
4 Answers
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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0It 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. – 2015-05-24
Theorems and Problems in Functional Analysis has a lot of problems with hints and solutions.
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2this book is hard – 2013-11-11
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:
Bernard Gelbaum's Problems in Real and Complex Analysis has a chapter on topological vector spaces, which are functional analysis problems.