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Most textbooks I've seen so far are not concise enough for my taste and try to give way too much motivation. Or they're written with a too large focus on applications... Rudin wasn't bad contentwise, but the layout tells you it was 1991...

An example for a perfect textbook in my eyes would be the Analysis series of Amann/Escher (I have the German editions and assume the English ones aren't essentially different). They go into depth, don't babble around and are yet as general as possible in their definitions and proofs, without having one lose focus. The structure is very clear, too and beautifully built up.

Is there some textbook like this about functional analysis?

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  • $\begingroup$ Do you know Dirk Werner, "Funktionalanalysis"? $\endgroup$ – math12 Nov 24 '13 at 13:08
  • $\begingroup$ @math12: Yes, I know that one. I didn't like, that he didn't really go into weakly differentiable functions - he only gave an example for weakly differentiable functions on some interval $[a,b]$. I don't know if he does that frequently in his book. And there seem to be a lot of references to other books for certain proofs... Plus the formatting somehow didn't read that nicely (yeah I know, luxury problems... still :) ). $\endgroup$ – polynomial_donut Nov 24 '13 at 13:40
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    $\begingroup$ brezis analyse fonctionelle $\endgroup$ – Alexander Grothendieck Nov 24 '13 at 13:41
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    $\begingroup$ "Plus the formatting somehow didn't read that nicely" Kids today. What about typoscripts with hand-drawn greek letters and symbols like $\{,\int,\in$? Now get off my lawn ;) $\endgroup$ – Daniel Fischer Nov 24 '13 at 13:50
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    $\begingroup$ You could also have a look at Meise/Vogt. I don't remember how they treated Sobolev spaces etc. (honestly, I avoid those where I can, ugh), but it's excellent for the general theory of HLCS. $\endgroup$ – Daniel Fischer Nov 24 '13 at 13:56

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