most recent 30 from http://mathoverflow.net 2013-06-18T22:06:08Z http://mathoverflow.net/feeds/question/42665 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42665/alternative-for-kadison-and-ringroses-book Jiang 2010-10-18T16:13:10Z 2012-01-02T17:08:33Z

<p>I have read over the book by R. V. Kadison and J. R. Ringrose: Fundamentals of the theory of operator algebras. Vol 1, and have done most of the exercises in it. Now I want to find an alternative book for Vol 2, because I once heard that the content in this book is somewhat out of date and the theories are developed in a rather slow pace. Which book can I choose then? </p>

http://mathoverflow.net/questions/42665/alternative-for-kadison-and-ringroses-book/42701#42701 Martin Argerami 2010-10-18T21:57:32Z 2010-10-18T21:57:32Z

<p>I guess it depends a little on what you are looking for. </p> <p>If you want to pay attention to the C*-side, you may want to look at Davidson (very neat presentation of several key topics), or Murphy (maybe more basic, but a favourite in clarity). </p> <p>For the von Neumann side, an option to get started is Sunder: many things are done in factors, avoiding many complications tackled by Kadison. But if you are going to be into von Neumann algebras at all, I think that you need to have some familiarity with Kadison and with Takesaki. I usually find myself going back to those two fairly often. </p>

http://mathoverflow.net/questions/42665/alternative-for-kadison-and-ringroses-book/42716#42716 Andrew L 2010-10-18T23:44:11Z 2011-12-31T15:56:08Z

<p>A few years ago, a 2 volume advanced text on operator theory (vol. 50: "An invitation to operator theory"; vol. 51: "Problems in operator theory") came out by Y.A. Abramovich and C.D. Aliprantis which is supposed to be excellent and very up to date; it's the only account that gives a detailed treatment of ordered function spaces. A detailed description of the text can be found here:</p> <pre><code>http://www.ams.org/bookstore?fn=20&amp;arg1=analysis&amp;ikey=GSMSET. </code></pre> <p>I haven't done more then browse it and most of it's over my head, but it definitely is worth a look. </p>

http://mathoverflow.net/questions/42665/alternative-for-kadison-and-ringroses-book/42747#42747 Matthew Daws 2010-10-19T07:32:25Z 2010-10-19T07:32:25Z

<p>I'll add a specific entry for Takesaki's books. I learnt what von Neumann theory I know from these books. Especially volume 2 is a very nice, and concise, guide to an awful lot of the theory around Tomita-Takesaki and Connes' theory of weights.</p> <p>If you are interested in Tomita-Takesaki, in a gentler fashion, then the old books by Stratila are nice. In particular, they explain the unbounded operator theory somewhat more than Takesaki does.</p> <p>But it really depends what the original interest is: if you want to get into modern C*-algebra theory, then Takesaki is not the way to go.</p> <p>Finally, for reference, the recent book by Blakadar is wonderful, and is a great place to look for something, before reading up in more detail somewhere else.</p>

http://mathoverflow.net/questions/42665/alternative-for-kadison-and-ringroses-book/42769#42769 Jon Bannon 2010-10-19T11:53:22Z 2010-10-19T11:53:22Z

<p>It depends on what you'd like to know. Above answers suggest Davidson and Blackadar for C*-algebras, and Takesaki for some more detailed theory of von Neumann algebras. These are excellent suggestions. </p> <p>I'd like to add that if you want to learn more about finite von Neumann algebras/factors, you may find it helpful to read chapters 6-9 of Kadison and Ringrose, and then have a look at <em>Finite von Neumann algebras and MASAs</em> by Sinclair and Smith. Then you perhaps should try to read some of Sorin Popa's recent papers and begin backfilling knowledge around these.</p>