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Paper   IPM / M / 15093
School of Mathematics
  Title:   Hilbert C*-bimodules of finite index and approximation properties of C*-algebras
1.  Marzieh Forough
2.  Massoud Amini
  Status:   Published
  Journal: Glasg. Math. J.
  Vol.:  60
  Year:  2018
  Pages:   323-331
  Supported by:  IPM
Let A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A�??B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A�??B-bimodules,which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

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