From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3739 Path: news.gmane.org!not-for-mail From: Gabor Lukacs Newsgroups: gmane.science.mathematics.categories Subject: Re: C*-algebras Date: Sat, 28 Apr 2007 23:30:06 -0500 (CDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019493 10077 80.91.229.2 (29 Apr 2009 15:38:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:38:13 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Apr 29 22:19:54 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 29 Apr 2007 22:19:54 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HiKTc-00065G-E8 for categories-list@mta.ca; Sun, 29 Apr 2007 22:14:52 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 26 Original-Lines: 56 Xref: news.gmane.org gmane.science.mathematics.categories:3739 Archived-At: Dear Bas, > It seems hard to find references to a categorical treatment of > C*-algebras. I am surprised to hear that. Here are a few, which I am almost sure that=20 you are already familiar with: D. H. Van Osdol. C*-algebras and cohomology. In Categorical topology (Toledo, Ohio, 1983), volume 5 of Sigma Ser. Pure Math., pages 582-587. Heldermann, Berlin, 1984. J. Wick Pelletier and J. Rosick=B4y. On the equational theory of=20 C*-algebras. Algebra Universalis, 30(2):275-284, 1993. Joan Wick Pelletier and Ji.r=B4. Rosick=B4y. Generating the equational th= eory=20 of C*-algebras and related categories. In Categorical topology and its=20 relation to analysis, algebra and combinatorics (Prague, 1988), pages=20 163-180. World Sci. Publishing, Teaneck, NJ, 1989. Edward G. Effros and Zhong-Jin Ruan. Operator spaces, volume 23 of London Mathematical Society Monographs. New Series. The Clarendon Press Oxford University Press, New York, 2000. [This last one is not categorical, but it contains some results concernin= g=20 the tensor products that can easily be interpreted categorically.] You my find a brief summary of the categorically interesting points in=20 Chapter 8 of my PhD thesis: http://at.yorku.ca/p/a/a/o/41.pdf > Concretely, there are several tensor products on C*-algebras. Which one= =20 > is `the right one' from a categorical perspective? This is an interesting question, but I suspect that you may find a clue t= o=20 answer this question here: Theodore W. Palmer. Banach algebras and the general theory of *-algebras.= =20 Vol. 2, volume 79 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 2001. I hope that my answers are of some help to you. Best wishes, Gabi