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Hilbert -modules over \varSigma ^*-algebras

Tom 235 / 2016

Clifford A. Bearden Studia Mathematica 235 (2016), 269-304 MSC: 46L08, 46L05, 46H25. DOI: 10.4064/sm8616-9-2016 Opublikowany online: 21 October 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.

Autorzy

  • Clifford A. BeardenDepartment of Mathematics
    University of Houston
    Houston, TX 77204-3008, U.S.A.
    e-mail

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