A number of other Russian books also come close to what you ask for. The two that came to my mind first are:

[Theorems and problems in functional analysis][1] by Kirillov and Gvishiani

[Abel's theorem in problems and solutions][2] by Alekseev (based on [Arnol'd][3]'s lectures)


  [1]: http://books.google.com/books?id=XAApQAAACAAJ
  [2]: http://books.google.com/books?id=GI_SmiYsh0UC
  [3]: http://en.wikipedia.org/wiki/Vladimir_Arnold