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.
|Journal||Archiv der Mathematik|
|Publication status||Published - 1 Jan 2009|
- Completely bounded module homomorphisms
- Haagerup tensor product
- Local multiplier algebra
- Maximal C*-algebra of quotients
- Strong Morita equivalence