Operator algebras

[hellfire]

I am looking for a book to study operator algebras: linear spaces, banach-, C*- and von Neumann-algebras, etc. on an introductory level for physics. After searching a bit it seems that "Operator Algebras: Theory of C*-Algebras and von Neumann Algebras" B. Blackadar should be a good choice. This is also the reference mentioned in the wikipedia article. Does anyone know this book? Any other suggestions?.. may be there are also some online notes somewhere?

 

[morphism]

What's your background in functional analysis? E.g. do you know things like the Hahn-Banach theorem and the Riesz functional calculus?

 

[MathematicalPhysicist]

Morphism, I guess it's understandable from him that he's a novice.

Anyway, for books there are Michael Read's 4 volumes series, Rudin's text in functional analysis and vitali milman's text.
Rudin's text is very expensive, try finding a copy at your library or the net.

 

[morphism]

I just wanted to gauge how much of a novice he is.

By the way, Rudin's book is probably not what he's looking for. It's not really a book on operator algebras as much as it is a book on elementary functional analysis; e.g. it contains no real mention of operator topologies or von Neumann algebras. Also I don't think it has the noncommutative Gelfand-Naimark theorem in it either (I'm not 100% positive - but this is what I remember), and this is one of the most basic results of the theory of C*-algebras.

 

[MathematicalPhysicist]

But you can find this stuff in Read's book, correct?

Well ofcourse the poster can search in amazon, google and his library for textbooks in this stuff.

I just know that at my univ, a course in hilbert spaces and operator theory is a prequisite to the course functional analysis, so this is why I thought naively that these books cover this material.

Anyway I haven't yet learned it, learning for both maths physics is great by its own sake, but there are overlaps in hours so it makes it very hard to acquire the knowledge even after 3 years at univ (this year is my third).

 

[hellfire]

Some results in functional analysis such as the Hahn-Banach theorem need not be part of the book. I am not very familiar with it and its consequences, but it is not completely new for me. I have however access to other functional analysis references to work on that if necessary.

The book I am looking for should contain the contents I have mentioned: Banach-, C*- and von Neumann-algebras, GNS construction, etc. It should not be difficult to follow, and, moreover, it should be available in amazon or similar. I have already searched in amazon, google and found some references but I would like to know your opinion. Thanks.

By the way I was not able to find Rudin, Milman nor Read. Please give me also the title of the books or a link.

 

[morphism]

Try volume 1 of Kadison and Ringrose (available online through not-so-legal means). Two other good books are Douglas's Banach Algebra Techniques in Operator Theory and Pedersen's Analysis Now, but they are terse and not 'easy reads' (not that K&R is).

LW Marcoux also has notes posted online, available http://www.math.uwaterloo.ca/~lwmarcou/Preprints/PMath810Notes.pdf. And VS Sunder has his book, Functional Analysis, available for free on his website. Both have all the things you mentioned.

Rudin's book is here. I don't know what the other two are.

 

[MathematicalPhysicist]

Well, now I'm not so sure the book by read covers what you want, anyway, these are two authors:
Michael Read and Barry Simon, Methods of modern mathematical physics.

The book by vitali milman is in functional analysis, but from looking at its contents it does have a chpater on banach algebras, the name of the book is introduction to functional analysis.

The former book series is quite pricey, perhaps maths publishers think maths students are richer than your avergae bear.