Where can I find challenging functional analysis problems for self-study?

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Does anyone know of where I should look to find lots of good functional analysis problems? I am currently reading Kreyszig which has great commentary, but the majority of the exercises are simple.
 
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There are lots of good GTM books with challenging problems, e.g. Conway and Pedersen. In my opinion Pedersen's problems are too challenging, in the sense that it's almost impossible to do most of them if this is your first functional analysis course.
 
Thanks. I'm going to take your advice and buy Conway.
 
I just picked up Exercises in Functional Analysis by Costara and Popa. This will be invaluable for me, since I'm self-studying, so its always nice to be able to check my work if I get stuck.