The maximal C*-algebra of quotients as an operator bimodule

Pere Ara, Martin Mathieu, Eduard Ortega

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Abstract

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product A ⊗h labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved. © 2009 Birkhäuser Verlag Basel/Switzerland.
Original languageEnglish
Pages (from-to)405-413
JournalArchiv der Mathematik
Volume92
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Completely bounded module homomorphisms
  • Haagerup tensor product
  • Local multiplier algebra
  • Maximal C*-algebra of quotients
  • Strong Morita equivalence

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