How do I begin learning functional analysis?

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How do I begin learning functional analysis?

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(s)kill yourself

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>>7793092

read a book

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>>7793092

study set theory then group theory then abstract algebra then real analysis then complex analysis and then you can begin studying functional analysis

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>>7793092

You should know some basics before you start in particular real analysis, linear algebra (with respect to vector spaces) and some elemtary concepts from (point set) topology otherwise you might have to look up a lot of things while trying to get into functional analysis itself. If you ´re looking for a book to start with, I´d recommend Yoshida as a classic or Werner (but I don´t know if there is an english version of it). I also really like the writing style of Brezis but I only ever read his book and functional analysis and PDEs not the one about functional analysis.

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>>7793146

Set theory and complex analysis are not needed for functional analysis.

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https://www.youtube.com/playlist?list=PL554B877A872B4F94

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>>7793320

Is abstract algebra needed? I would have thought analysis and linear algebra were needed

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>>7793355

>Is abstract algebra needed?

For an introduction no. But once you get to more advanced topics like representation theory on Hilbert spaces and operator algebras, you'll need some algebra background.

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>>7793187

I know vector spaces and topology of the real numbers.

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>>7793092

Introductory Functional Analysis with Applications by Erwin Kreyszig

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The progression I would suggest is the following: real analysis, linear algebra, complex analysis and measure theory. Then find a book, I used foundations of modern analysis by avner friedman. It's pretty compact tho, written for 3rd year mathematics students. Someone suggested Introductory Functional Analysis by Erwin Kreyszig, I haven't used it but I heard good things...

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>>7793744

Complex analysis is uneeded.

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>>7793092

Understand what type of data you have and what question you want to answer with them.

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