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Paper   IPM / M / 15562
School of Mathematics
  Title:   Frame-less Hilbert C*-modules
  Author(s):  Mohammad Bagher Asadi (Joint with M. frank and Z. Hassanpour-Yakhdani)
  Status:   Published
  Journal: Glasg. Math. J.
  Vol.:  61
  Year:  2019
  Pages:   25-31
  Supported by:  IPM
We show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A1-module admitting no frames, where A1 is the unitization of A. In particular, there exists a frame-less Hilbert C*-module over the C*-algebra K(l2) \dotplus\mathbbCIl2.

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