A book for problems in Functional Analysis I want to know if there's any book that categorizes problems by subjects of Functional Analysis.
I'm studying Functional Analysis now a days and I really need to solve some problems in order to assure myself that I've really understood the concepts and definitions.
For example: problems related to the Hahn-Banach theorem or Banach Spaces or Hilbert Spaces or related subjects. 
 A: P. Wojtaszczyk, "Banach spaces for analysts", Cambridge studies in advanced mathematics contains problems from many areas of analysis. The hints in the back make the problems easier without giving everything away.
A: C. Costara, Dumitru Popa: Exercises in Functional Analysis
A: Aufgaben und Lehrsätze aus der Analysis, G. Pólya & G. Szegö
Problems and theorems in analysis, G. Pólya & G. Szegö.
Translation by D. Aeppli
A: Another classical book is Theorems and problems in functional analysis by Kirillov and Gvishiani.
A: MR0675952 (84e:47001)
Halmos, Paul Richard
A Hilbert space problem book.
Second edition. Graduate Texts in Mathematics, 19. Encyclopedia of Mathematics and its Applications, 17. Springer-Verlag, New York-Berlin, 1982. xvii+369 pp. ISBN: 0-387-90685-1 
A: I would like to add to the list my favorite book on Classical Functional Analysis:
Dunford, Nelson; Schwartz, Jacob T. Linear operators. Part I. General theory. With the assistance of William G. Bade and Robert G. Bartle. Reprint of the 1958 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1988. xiv+858 pp. ISBN: 0-471-60848-3 
This book contains a plenty of exercises, which allow to check understanding and much more.     
A: Also Brezis' book Functional analysis, Sobolev spaces and partial differential equations contains a lot of nice and interesting functional analytical problems.
A: I realy like the exercises in Gert Pedersen's book Analysis Now.
A: If you can refrain yourself from looking at the hints (which are almost complete solutions for the most part), Functional analysis and infinite-dimensional geometry
 By Marián J. Fabian, et al. is a very good book with lots of exercises.
A: Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form 
 I. M. Glazman , Ju. I. Ljubic 
You will learn (finite)functional analysis by solving problems.(not the easiest way..)
http://www.amazon.com/Finite-Dimensional-Linear-Analysis-Systematic-Presentation/dp/0486453324/ref=sr_1_5?ie=UTF8&s=books&qid=1270895647&sr=1-5
A: A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).
Great collection of problems with solutions.
