I would suggest the book by Haim Brezis: *Analyse fonctionnelle, theorie et applications*. It was recently translated into English and you can find the information for the English translation [here][1].


  [1]: http://www.amazon.com/Functional-Analysis-Differential-Equations-Universitext/dp/0387709134/ref=sr_1_1?ie=UTF8&qid=1312865620&sr=8-1