Asking for reference for challenging problems for Functional Analysis 1st course

You may follow the following references:

$1.~~$ "Theorems and Problems in Functional Analysis" by A. A. Kirillov, A. D. Gvishiani
$2.~~$ "Problems in Real and Functional Analysis" by Alberto Torchinsky
$3.~~$ "Theorems and Problems in Functional Analysis" by J. D. Knowles
$4.~~$ "A Glimpse at Hilbert Space Operators" by Paul R. Halmos

These books contains many standard problems. Most of the problems are hard but very good once it is done. I think you may get benefit from here so just try it.


I'll recommend Exercises in Analysis, Part I by Gasiński, and Papageorgiou. It's a brilliant source of thoughtful and challenging exercises in mathematical analysis; starting from basics of metrics spaces, then topology, measure theory and functional analysis. Also, it comes with full solutions.

For more advanced topics there's also a second part too by the same authors.

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Analysis

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