On a generalization of $W^*$-modules

Volume 91 / 2010

David P. Blecher, Jon E. Kraus Banach Center Publications 91 (2010), 77-86 MSC: Primary 47L30, 47L45, 46L08; Secondary 16D90, 47L25. DOI: 10.4064/bc91-0-4


a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the $W^*$-modules (that is, Hilbert $C^*$-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.


  • David P. BlecherDepartment of Mathematics
    University of Houston
    Houston, TX 77204-3008, U.S.A.
  • Jon E. KrausDepartment of Mathematics
    State University of New York at Buffalo
    Buffalo, NY 14260-2900, U.S.A.

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