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/ ]