On Mon, May 03, 2010 at 03:18:57PM -0400, Michael Barr wrote:
Way back, John Isbell told me that the theory of C*-algebras could be dnoe with a batch of finitary operations such as convex sum, product, and maybe others plus exactly one omega-ary operation that takes {x_i} to \sum 2^{-i}x_i. Does anyone know if John ever published this and where?
Yes he did. @article{MR686798, title = {Generating the algebraic theory of {$C(X)$}}, author = {Isbell, John}, eprint = {http://dx.doi.org/10.1007/BF02483718}, fjournal = {Algebra Universalis}, issn = {0002-5240}, journal = {Algebra Universalis}, mrclass = {08A65 (03G25 03G30 18C10)}, mrnumber = {MR686798 (84e:08004)}, mrreviewer = {A. Kh. Kushkule{\u\i}}, pages = {153-155}, url = {http://dx.doi.org/10.1007/BF02483718}, volume = {15}, year = {1982}, } The operations are laid out: the unit, multiplication by -1, multiplication, a funny not-quite-doubling operation (x -> (2x v 1) n (-1)), and the one you mention above. (I learnt about this from the references of the paper by Pelletier and Rosicky, MR1223636) Andrew [For admin and other information see: http://www.mta.ca/~cat-dist/ ]