From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3745 Path: news.gmane.org!not-for-mail From: Jeff Egger Newsgroups: gmane.science.mathematics.categories Subject: Re: C*-algebras Date: Wed, 2 May 2007 13:03:55 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241019497 10110 80.91.229.2 (29 Apr 2009 15:38:17 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:38:17 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed May 2 14:20:37 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 02 May 2007 14:20:37 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HjIQw-0007Nz-Cc for categories-list@mta.ca; Wed, 02 May 2007 14:16:06 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 5 Original-Lines: 38 Xref: news.gmane.org gmane.science.mathematics.categories:3745 Archived-At: --- Miles Gould wrote: > Jeff Egger gave a talk on some of these ideas at the Nice PSSL - I'm > somewhat surprised he hasn't replied to this thread. I'm usually too shy to post to the mailing list, so I wrote Bas Spitters a personal reply instead. In this case, though, I have to set the record straight... > IIRC, the category > of operator algebras is an involutive monoidal category with respect to > one or other of the tensor products, and C*-algebras are exactly the > involutive monoids w.r.t. this tensor product. Can't remember which one > it was, though. The category of operator _spaces_ admits a (non-trivial) involutive monoidal structure---by which I mean a (non-commutative) monoidal structure together with a _covariant_ involution that reverses the order of tensoring. [Regarding a monoidal category as a one-object bicategory B, this means that the involution relates B with B^{op} rather than with B^{co}.] The tensor product is called the _Haagerup_ tensor product, and the involution I considered is the so-called _opposite_ operator space structure applied to the conjugate vector space. I had conjectured that involutive monoids in this involutive monoidal category (which, for the purposes of this mail, I shall call involutive operator algebras) are the same as C*-algebras, but eventually I discovered a counter-example which showed that involutive operator algebras are strictly more general than C*-algebras. (This was the direction which had less concerned me!) I apologise to anyone to whom I failed to mention this counter-example. Cheers, Jeff. Ask a question on any topic and get answers from real people. Go to Yahoo! Answers and share what you know at http://ca.answers.yahoo.com