A good book of functional analysis - MathOverflow

A good book of functional analysis

2011-08-09T01:24:16Z

I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the basics). What I am looking for is good books that I could understand to go deeper in this areas, what do you recommend? (I can read in Spanish, English, French and German)

Answer by Chris Godsil for A good book of functional analysis

2011-08-09T01:30:35Z

I am not an analyst of any sort, so you do not need to listen to me, but I really like Lax's "Functional Analysis".

Answer by Salvatore Siciliano for A good book of functional analysis

2011-08-09T01:47:10Z

I am an algebraist and not an analyst, however my favourite book on this area is "Walter Rudin: Functional Analysis".

Answer by Abhinav Kumar for A good book of functional analysis

2011-08-09T01:51:17Z

John B. Conway's "A course in functional analysis" is also pretty decent.

Answer by Tony Huynh for A good book of functional analysis

2011-08-09T03:05:20Z

There's no reason to listen to me either, but for delving a bit deeper, you might want to check out T. W. Körner's Fourier Analysis. The book consists of very short (often just a couple of pages) chapters which contain gems like computing the age of the Earth.

Answer by Chandrasekhar for A good book of functional analysis

2011-08-09T03:05:33Z

Some of the good books are:

Elements of the Theory of Functions and Functional Analysis by Kolmogorov, Fomin.

Functional Analysis, by F.Riesz and Nagy.

Functional Analysis : Spectral Theory by V.Sunder. Freely available here.

Analysis now. By Gert Kjeargård Pedersen. (As suggested by Theo Buehler at $\textbf{Math.SE}$

Stein, Elias; Shakarchi, R. (2011). Functional Analysis: An Introduction to Further Topics in Analysis. Princeton University Press. ISBN 0691113874.

Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext) by Haim Brezis.

Elementary Functional Analysis by Georgi E. Shilov.

Introductory Functional Analysis with Applications by Erwin Kreyszig.

Notes on Functional Analysis by Rajendra Bhatia. (Hindustan Book Agency.)

Functional Analysis by S.Kesavan. ( Hindustan Book Agency.)

Elementary functional analysis By Barbara D. MacCluer

Functional analysis: an introduction By Yuli Eidelman, Vitali D. Milman, Antonis Tsolomitis (AMS)

Principles of functional analysis By Martin Schechter. (AMS)

You may also want to see this thread: Problem books in Functional Analysis

$\textbf{Note.}$ The books which are written in Italics are the ones which I have read partially. The ones which are not in Italics are the ones which I have come to know (by friends, teachers) are good books in Functional Analysis. Also, I really don't know which publisher actually publishes the book in foreign edition written by Kesavan and Bhatia.

Answer by Anatoly Kochubei for A good book of functional analysis

2011-08-09T04:28:18Z

When I was studying, I was influenced much by K. Yosida's "Functional Analysis".

Answer by Mahdi Majidi-Zolbanin for A good book of functional analysis

2011-08-09T04:57:40Z

I would suggest the book by Haim Brezis: Analyse fonctionnelle, theorie et applications. It was recently translated into English and you can find the information for the English translation here.

Answer by Angelo Lucia for A good book of functional analysis

2011-08-09T07:54:57Z

Apart from the classics already mentioned (Yosida, Brezis, Rudin), a good book of functional analysis that I think is suitable not only as a reference but also for self-study, is Fabian, Habala et al. Functional Analysis and Infinite-Dimensional Geometry. It has a lot of nice exercises, it's less abstract than the usual book and provides a lot of "concrete" theorems.

And I'm not sure about it, but I heard there is a spanish translation (the original is of course in english).

Answer by Pieter Naaijkens for A good book of functional analysis

2011-08-09T08:09:58Z

You might be interested in "Analysis Now" by Pedersen. A very nice book on graduate level analysis in my opinion. It covers some areas of functional analysis as well.

Answer by Amritanshu Prasad for A good book of functional analysis

2011-08-09T09:11:54Z

Zimmer's Essential Results of Functional Analysis is a very interesting read, specially if you already know some basic stuff in functional analysis.

Answer by John D. Cook for A good book of functional analysis

2011-08-09T11:10:20Z

I'd recommend the Dunford and Schwartz. It's a classic. It's huge -- three volumes. But you don't have to read the whole series cover-to-cover. If you read half of the first volume, you'll learn about as much as reading many other books on functional analysis. Volume 1 alone is big, but it's easy to read for a book on its subject.

Answer by Daniel Pape for A good book of functional analysis

2011-08-09T15:36:17Z

The book on Functional Analysis by Meise and Vogt

http://books.google.de/books?id=FavCGyUirRkC&dq=Meise+Vogt&hl=de&ei=F1JBTpPXItOx8QOdtPm4CQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDEQ6AEwAQ

is quite comphrensive and contains beside standard functional analysis more advanced sections on the theory of locally convex spaces. There is also a German version if you want to improve your German by reading both together.

Answer by Mark Meckes for A good book of functional analysis

2011-08-09T16:20:08Z

Since you read German, my favorite is Funktionalanalysis by Dirk Werner. It's not necessarily comprehensive, but it covers a lot, has extensive historical remarks, and is extremely well-written -- I find it more readable than most math books in English (my first language).

Answer by Andrew for A good book of functional analysis

2011-08-12T06:01:24Z

I personally like a recent book of Helemskii Lectures and Exercises on Functional Analysis. One of the differences with other books on the subject is that it uses the categorical point of view. The author starts with a very brief introduction to the category theory and uses this language throughout the book. It's a sort of modern core of FA book, with a sidelines to some physics applications and of historic nature, a terse advertisement of the quantum functional analysis and so on (but there is no measure theory, Radon Nikodym theorem etc. which are elaborated in many excellent old textbooks.) Also it gives somewhat broader picture of FA sketching some directions and stating from time to time theorems without proofs 'that every student should know'.

Answer by Fredrik Meyer for A good book of functional analysis

2011-09-01T22:22:54Z

In a course I'm taking now, we're using Gerald Teschl's "Topics in Real and Functional Analysis". It seems like you may already know the first few chapters, however.

It's quite well written, and is free: http://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html