From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1314 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: banach operations Date: Sat, 1 Jan 2000 11:48:43 -0500 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017744 30683 80.91.229.2 (29 Apr 2009 15:09:04 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:09:04 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Sat Jan 1 14:56:55 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00373 for categories-list; Sat, 1 Jan 2000 13:42:59 -0400 (AST) X-Authentication-Warning: triples.math.mcgill.ca: barr owned process doing -bs X-Sender: barr@triples.math.mcgill.ca Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 16 Xref: news.gmane.org gmane.science.mathematics.categories:1314 Archived-At: Peter's last posting reminded me of something that may or may not be relevant. Sometime in the previous millennium (actually, around 3 decades ago) John Isbell made an observation that amounted to the statment that the equational theory of the unit ball functor of banach spaces (which has many more algebras than banach spaces) could be described by negation and an aleph_0-ary operation that takes {x_i} to \sum_{i=1}^\infty 2^{-i}x_i (and appropriate equations). Now a midpoint algebra with involution, as described by Peter, has all such finitary sums and if you also assume it complete, I think it is likely exactly a model of the banach space theory. Michael