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Hello everybody,

I want to know if there's any book that categorizes problems by subjects of Functional Analysis. I'm studying Functional Analysis now a days and I really need to solve some problems in order to assure myself that I've really understood the concepts and definitions. For example: problems related to the Hahn-Banach theorem or Banach Spaces or Hilbert Spaces or ...

Thanks in advance.

edited Jun 25 2010 at 10:32

Andrey Rekalo

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3 revisions, 3 users
Soheil Malekzadeh 100%

	You might also check out "Banach Algebra Techniques in Operator Theory" by Douglas. The book extends beyond the material of a first course in functional analysis, but the first chapter (on Banach Spaces) and the third chapter (on Hilbert Spaces) cover the basic theory in detail from scratch. Both chapters have a huge and excellent collection of problems at the end. The fourth chapter has, in my opinion, the best introductory treatment of spectral theory around (and the best collection of exercises at the end), and the fifth has an excellent treatment of compact operators and index theory. – Paul Siegel Jun 25 2010 at 20:40
	Thanks Paul. I have this book and I have to say that it's a fantastic one. – Soheil Malekzadeh Jun 27 2010 at 6:39

mathphysicist · Accepted Answer · 2010-01-31 17:19:44Z UTC

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Another classical book is Theorems and problems in functional analysis by Kirillov and Gvishiani.

answered Jan 31 2010 at 17:19

mathphysicist

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This is exactly what I was searching for. Thanks. – Soheil Malekzadeh Feb 11 2010 at 19:20

Chandan Singh Dalawat · Answer 2 · 2010-01-31 13:24:27Z UTC

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MR0675952 (84e:47001) Halmos, Paul Richard A Hilbert space problem book. Second edition. Graduate Texts in Mathematics, 19. Encyclopedia of Mathematics and its Applications, 17. Springer-Verlag, New York-Berlin, 1982. xvii+369 pp. ISBN: 0-387-90685-1

answered Jan 31 2010 at 13:24

Chandan Singh Dalawat

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I would have proposed the same book. It's really excellent! – Martin Brandenburg Jan 31 2010 at 14:02

Indeed a classic. However, I haven't looked at it in years. I wonder if it becoming dated? (Of course mathematics books generally age well, but …) – Harald Hanche-Olsen Jan 31 2010 at 15:00

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Halmos' book is indeed excellent, but it deals only with operator theory on Hilbert spaces. – Bill Johnson Jan 31 2010 at 19:36

Gerald Edgar · Answer 3 · 2010-01-31 18:21:14Z UTC

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Aufgaben und Lehrsätze aus der Analysis, G. Pólya & G. Szegö

Problems and theorems in analysis, G. Pólya & G. Szegö. Translation by D. Aeppli

answered Jan 31 2010 at 18:21

Gerald Edgar

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Bill Johnson · Answer 4 · 2010-01-31 18:48:40Z UTC

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P. Wojtaaszczyk, "Banach spaces for analysts", Cambridge studies in advanced mathematics contains problems from many areas of analysis. The hints in the back make the problems easier without giving everything away.

answered Jan 31 2010 at 18:48

Bill Johnson

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	While I've come to appreciate Wojtaszczyk's book more since my PhD days, I personally found it more suitable for dipping into (after one had learned the basics) than for learning from. But this is very much just a matter of my personal taste. – Yemon Choi Jan 31 2010 at 19:45
	I agree, Yemon. For the basics, the exercises in virtually any book on Real Analysis (e.g. Folland) are fine. Other sources are old Real Analysis qualifying exams, which many departments have on their web sites. – Bill Johnson Jan 31 2010 at 20:43

MTS · Answer 5 · 2010-01-31 19:44:44Z UTC

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I realy like the exercises in Gert Pedersen's book Analysis Now.

answered Jan 31 2010 at 19:44

MTS

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Seconded! Petersen's book is great. – userN Jun 25 2010 at 19:25

Bunyamin Sari · Answer 6 · 2010-01-31 20:32:47Z UTC

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If you can refrain yourself from looking at the hints (which are almost complete solutions for the most part), Functional analysis and infinite-dimensional geometry By Marián J. Fabian, et al. is a very good book with lots of exercises.

answered Jan 31 2010 at 20:32

Bunyamin Sari

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pi2000 · Answer 7 · 2010-04-10 10:45:39Z UTC

Finite-Dimensional Linear Analysis: A Systematic Presentation in Problem Form I. M. Glazman , Ju. I. Ljubic You will learn (finite)functional analysis by solving problems.(not the easiest way..) http://www.amazon.com/Finite-Dimensional-Linear-Analysis-Systematic-Presentation/dp/0486453324/ref=sr_1_5?ie=UTF8&s=books&qid=1270895647&sr=1-5

A book for problems in Functional Analysis

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