I have completed Baby Rudin about one year ago. Right now I am studying abstract algebra from I.N. Herstein's "Topics in Algebra". Also I would like to strengthen my knowledge on Functional Analysis since my background on that branch of math is quite poor.

Can anyone suggest good book with visual examples, good problems in order to study that abstract branch of mathematics?

My eventual aim is to study T.Tao "Additive combinatorics" which require good knowledge of functional analysis, abstract algebra and others.

  • $\begingroup$ If you liked Baby Rudin go on with Rudin's Functional Analysis. $\endgroup$ – Jochen Nov 10 '17 at 7:44
  • $\begingroup$ books.google.dk/books/about/… take a look. $\endgroup$ – Gibbs Nov 10 '17 at 7:51
  • $\begingroup$ @Jochen, Baby Rudin was quite good except multivariable calculus. Have you ever read Rudin's Functional Analysis? $\endgroup$ – ZFR Nov 10 '17 at 8:18

I suggest A course in Functional Analysis, by John B. Conway.

  • $\begingroup$ Does it have problems theoretical and computational? $\endgroup$ – ZFR Nov 10 '17 at 8:34
  • $\begingroup$ @RFZ Yes, it has. And it has lots of problems. $\endgroup$ – José Carlos Santos Nov 10 '17 at 8:38
  • $\begingroup$ Have you ever read Rudin's Functional Analysis? $\endgroup$ – ZFR Nov 10 '17 at 8:39
  • $\begingroup$ @RFZ Yes. And I like it. But I think that Conway's is more readable. $\endgroup$ – José Carlos Santos Nov 10 '17 at 8:40
  • $\begingroup$ As I said above my aim is to gain knowledge on functional analysis in order to grasp material from Tao's book. What about Shakarchi and Stein's book? $\endgroup$ – ZFR Nov 10 '17 at 8:48

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