Infinitary operations on C(X)
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? Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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/ ]
John Isbell published Generating the algebraic theory of C(X), Alg. Univ. 15 (1982), 153-155 With Joan Pelletier, we wrote Generating the monadic theory of C*-algebras and related categories, Proc. Categ. Top. and Appl., World-Scientific 1989, 163-180; On the equational theory of C*-algebras, Alg. Univ. 30 (1993), 275-284. Jiri Rosicky ----- Forwarded message from Michael Barr <barr@math.mcgill.ca> -----
Date: Mon, 3 May 2010 15:18:57 -0400 (EDT) From: Michael Barr <barr@math.mcgill.ca> To: Categories list <categories@mta.ca> Subject: categories: Infinitary operations on C(X)
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?
Michael
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
----- End forwarded message ----- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (3)
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Andrew Stacey -
Jiri Rosicky -
Michael Barr