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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.

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  • $\begingroup$ If you liked Baby Rudin go on with Rudin's Functional Analysis. $\endgroup$
    – Jochen
    Commented Nov 10, 2017 at 7:44
  • $\begingroup$ books.google.dk/books/about/… take a look. $\endgroup$
    – Gibbs
    Commented Nov 10, 2017 at 7:51
  • $\begingroup$ @Jochen, Baby Rudin was quite good except multivariable calculus. Have you ever read Rudin's Functional Analysis? $\endgroup$
    – RFZ
    Commented Nov 10, 2017 at 8:18

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

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  • $\begingroup$ Does it have problems theoretical and computational? $\endgroup$
    – RFZ
    Commented Nov 10, 2017 at 8:34
  • $\begingroup$ @RFZ Yes, it has. And it has lots of problems. $\endgroup$
    – José Carlos Santos
    Commented Nov 10, 2017 at 8:38
  • $\begingroup$ Have you ever read Rudin's Functional Analysis? $\endgroup$
    – RFZ
    Commented Nov 10, 2017 at 8:39
  • $\begingroup$ @RFZ Yes. And I like it. But I think that Conway's is more readable. $\endgroup$
    – José Carlos Santos
    Commented Nov 10, 2017 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? $\endgroup$
    – RFZ
    Commented Nov 10, 2017 at 8:48
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I think that " Introductory functional analysis with applications - ‎Kreyszig " is one of the best books for self learning functional analysis.

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