Where can I find challenging functional analysis problems for self-study?

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Discussion Overview

The discussion centers on finding challenging problems in functional analysis for self-study purposes. Participants share resources and recommendations for books that contain exercises suitable for various levels of understanding in the subject.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant inquires about sources for challenging functional analysis problems, expressing that the exercises in Kreyszig are too simple.
  • Another participant suggests looking into Graduate Texts in Mathematics (GTM) books, specifically mentioning Conway and Pedersen, while noting that Pedersen's problems may be excessively difficult for beginners.
  • A third participant indicates they will follow the suggestion to purchase Conway's book.
  • A fourth participant mentions acquiring "Exercises in Functional Analysis" by Costara and Popa, highlighting its usefulness for self-checking while studying.

Areas of Agreement / Disagreement

Participants generally agree on the need for more challenging problems, but there are differing opinions on the appropriateness of specific books for beginners, particularly regarding Pedersen's work.

Contextual Notes

Some participants express varying levels of difficulty associated with the recommended resources, indicating that the suitability of problems may depend on individual backgrounds and prior exposure to functional analysis.

Who May Find This Useful

Individuals self-studying functional analysis or seeking to deepen their understanding of the subject through challenging exercises.

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Does anyone know of where I should look to find lots of good functional analysis problems? I am currently reading Kreyszig which has great commentary, but the majority of the exercises are simple.
 
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There are lots of good GTM books with challenging problems, e.g. Conway and Pedersen. In my opinion Pedersen's problems are too challenging, in the sense that it's almost impossible to do most of them if this is your first functional analysis course.
 
Thanks. I'm going to take your advice and buy Conway.
 
I just picked up Exercises in Functional Analysis by Costara and Popa. This will be invaluable for me, since I'm self-studying, so its always nice to be able to check my work if I get stuck.
 

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