5
$\begingroup$

I have basically finished my grad school applications and have some time at hand. I want to start reading some classic papers in Operator Theory so as to breathe more culture here. I have read some when doing specific problems but have never systematically study the literature.

I wonder whether someone can give some suggestions on where to start since this area has been so highly-developed. Maybe to focus the attention let's, say, try to make a list of the top 20 must-read papers in Operator Theory. I believe this must be a very very difficult job, but maybe some more criteria would make it a little bit easier.

  1. I can only read English and Chinese and it's a pity since I know many of the founding fathers use other languages.

  2. I prefer papers that give some kind of big pictures, since I can always pick up papers related to specific problems when I need them (but this is not a strict restriction).

  3. I would like to focus on the theory itself, not too much on application to physics.

  4. I have already done a rather thorough study of literature related to the invariant subspace problem, so I guess we can omit this important area.

Thanks very much!

  • 0
    Must-read papers may be quite old and written in old style. I suggest you to read surveys, they will give you the desired big picture and a lot of references.2012-11-27
  • 0
    @Norbert Great advice! Are there some surveys you would recommend?2012-11-28
  • 0
    A survey of operator algebras, Irving Kaplansky, R. L. Jeffery, Albert John Coleman, Alexandre Grothendieck. Authors are awesome!2012-11-28
  • 1
    Operator Algebras. Theory of $C^*$-algebras and von Neumann Algebras. Bruce Blackadar. This is a very compehensive treatment on general theory of $C^*$ and $W^*$ algebras.2012-11-28
  • 0
    @Norbert Great advice! But it seems even these surveys are rather old and I cannot actually find them in the local library nor online.2012-11-28
  • 0
    The first one survey is quite old (1971), the second one is very new (2010)2012-11-28
  • 0
    @Norbert Well, I can find neither of them. What a pity! It is amazing that Kaplansky, Coleman and Grothendieck once coauthored a survey.2012-11-28
  • 0
    @Norbert: Are you sure Kaplansky wasn't the sole auther of the first article? I haven't seen it, but would like to. Google scholar and others say that it was published with different articles by those other authors: "Survey of Operator Algebras:-I. Kaplansky; The Opening of Jeffery Hall-RL Jeffery, AJ Coleman; The Responsibility of the Scientist Today-A. Grothendieck" (Blackadar's book came out in 2005 or 2006 I think.)2012-11-29
  • 0
    @HuiYu, do papers on operator space theory count? If they do, take a look at G.Pisier's papers on Dixmier' problem and various other problems.2013-12-18

0 Answers 0