3
$\begingroup$

I have just started my phd program this semester, I have not worked before on $C^*-$algebras, my master was on Geometry. In my university only reading courses are offered. I have to learn $C^*-$algebras. I have not taken any courses on functional analysis too. I am studying the book " $C^*-$algebras and their automorphism groups" by Pedersen, I usually google each topic and take a look at Book by Murphy too. But I could not find a good resource that give me a good prospective, for example how should I use Gelfand representation in problems. I mean I am learning topics, but I cannot learn with deep depth that I can use stuff like tools in my work. And Also I undestood that Functional analysis is a priority for $C^*-$algebras, but I cannot find a good book for understanding deeply materials like weak and weak$^*$ topology. When I read theorems I understand them, but I could not understand these topics as well as I give ideas for solving theorems on my own, and I cannot enjoy studying. I would appreciate if you recommend me some good books for self studying both Functional analysis and $C^*-$algebras.

$\endgroup$
  • 2
    $\begingroup$ Definitely sounds like you need to read Conway's book, as suggested below. For weak and weak-$\ast$ topologies, have a look at Kesavan's "Functional Analysis". After that, Arveson's book on Spectral theory is worth a read. $\endgroup$ – Prahlad Vaidyanathan Oct 26 '16 at 9:28
3
$\begingroup$

My suggestion would be to consider Conway's "A Course in Functional Analysis". It even includes a basic chapter on C$^*$-algebras and von Neumann algebras.

Pedersen's book is wonderful in the sense of how concise he could write, but has a couple problems: one is that it is too deep, in a sense, so it is definitely hard for a beginner; and a second problem is that he (naturally) emphasized topics he did research, but that are not of much interest today.

You could also take a look at the first chapter in Davidson's C$^*$-algebras by Example.

$\endgroup$
  • $\begingroup$ Thanks very much for suggestions, is Davidson's book a good apporach for getting familiar with topics of research interest in operator algebras? $\endgroup$ – Sarah Smith Oct 23 '16 at 19:20
  • 1
    $\begingroup$ It is at least a good sample. It was written almost 30 years ago, though, so of course there are many things that C$^*$-algebra people pay attention to that are not mentioned. But it is important to first a good foundation. For a more comprehensive (but way less friendly) text take a look at Blackadar's Operator Algebras book. Also Rordam's and Lin's. $\endgroup$ – Martin Argerami Oct 23 '16 at 19:24

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.