Hilbert -modules over \varSigma ^*-algebras
Tom 235 / 2016
Streszczenie
A \varSigma ^*-algebra is a concrete C^*-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of C^*-modules over \varSigma ^*-algebras analogous to the class of W^*-modules (selfdual C^*-modules over W^*-algebras), and we are able to obtain \varSigma ^*-versions of virtually all the results in the basic theory of C^*- and W^*-modules. In the second half of the paper, we study modules possessing a weak sequential form of the condition of being countably generated. A particular highlight of the paper is the “\varSigma ^*-module completion,” a \varSigma ^*-analogue of the selfdual completion of a C^*-module over a W^*-algebra, which has an elegant uniqueness condition in the countably generated case.