I am in search for Functional Analysis Books.  I need a book which have lots of elementary problems.  I mean it should force us to think more which will give a deeper insight for functional analysis.  To be precise, I need lots of problems like Is $A$ open in the space $\ell^1$ with respect to norm $\|.\|_2$. Find a counterexample to this statement and etcetera.  I mean it shouldn't ask us trivial questions. It should ask us questions which will force us to think more and more from functional analysis
I am a EE grad. student who has had one undergraduate course in real analysis (which was pretty much the only pure math course that I have ever done). I would like to do a self study of some basic functional analysis so that I can be better prepared to take a graduate course in that material in my university. I plan to do that next fall so I do have some time to work through a book fully. Could some one recommend some good books to start working on this?   Thanks in advance
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