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I want to know functional analysis book like Terence tao's real analysis and measure theory book, full of intuition. I am aware of linear algebra, real analysis, measure theory, Probability theory.

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    $\begingroup$ You need to elaborate on what you mean by "full of intuition". Examples? Heuristics? As the question stands it looks like you're asking if Terry Tao has written a functional analysis textbook. $\endgroup$
    – Paul Siegel
    Commented Aug 9, 2015 at 12:04
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    $\begingroup$ I recently wrote a book on measure theory and functional analysis which I like to think includes a lot of intuition. But probably most authors would say this. $\endgroup$
    – Nik Weaver
    Commented Aug 9, 2015 at 23:33
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    $\begingroup$ The nicest book of functional analysis I can think of is still the 3 volume opus Linear Operators by Dunford and Schwartz. This book has a tone of examples. It has one drawback: it runs 2000 pages long. Still worth consulting. If you do not have the time or patience to read 2000 pages, then you should open Haim Brezis book on functional analysis. $\endgroup$
    – Liviu Nicolaescu
    Commented Oct 24, 2015 at 18:50
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    $\begingroup$ I like Reed & Simon's Methods of Mathematical Physics volume 1: Functional Analysis. Actually, all 4 volumes are excellent. $\endgroup$
    – J Tyson
    Commented Oct 25, 2015 at 21:04

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The book A. Ya. Helemskii, Lectures and exercises on functional analysis. AMS, Providence, RI, 2006 (translation from the Russian original) is IMHO well written and quite intuitive (check e.g. the MathSciNet review which is quite glowing).

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I'm at the moment enjoying the style of Graham Allan's Introduction to Banach Spaces and Algebras. It's packed with details and is I suppose somewhat dense, but the text is crisply clear and focused. There are also extensive notes. It doesn't assume any measure theory, but a background certainly helps, especially when it comes to the notes. Here's an MAA review- http://www.maa.org/publications/maa-reviews/introduction-to-banach-spaces-and-algebras

I had a little exposure from auditing a Coursera's Functional Analysis offering and a more thorough grounding in measure theory when I came to it, but with a modest overhead of effort you could get into it with less.

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Kreyszig is one I found most helpful.

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I believe 'Beginning Functional Analysis by Karen Saxe' is pretty good. The only downside could be that the book is quite elementary.

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