problem books in functional analysis

Theorems and Problems in Functional Analysis has a lot of problems with hints and solutions.

A $C_p$-Theory Problem Book: Topological and Function Spaces by Vladimir V. Tkachuk (2011). (I think all problems are solved in the main book.)

Also, this link at mathoverflow.net might be helpful.

The book Fabian, Habala, Hájek, Montesinos, Zizler: Banach Space Theory, The Basis for Linear and Nonlinear Analysis (CMS Books in Mathematics) has many exercises at the end of each chapter. It does not have solutions, but most of the exercises come with some hint (in some cases rather detailed). Google Books link, DOI: 10.1007/978-1-4419-7515-7

This book was also recommended in some other posts on this site:

• References for Banach Space Theory
• Book suggestion geometry of Banach spaces