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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!

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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. – Norbert Nov 27 '12 at 20:08
@Norbert Great advice! Are there some surveys you would recommend? – Hui Yu Nov 28 '12 at 2:41
A survey of operator algebras, Irving Kaplansky, R. L. Jeffery, Albert John Coleman, Alexandre Grothendieck. Authors are awesome! – Norbert Nov 28 '12 at 11:21
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. – Norbert Nov 28 '12 at 11:24
@Norbert Great advice! But it seems even these surveys are rather old and I cannot actually find them in the local library nor online. – Hui Yu Nov 28 '12 at 11:42

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