A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra Mloc(A) of A and its injective envelope I(A) is introduced. Various aspects of this maximal C*-algebra of quotients, Qmax(A), are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra A such that Mloc(Mloc(A)) ≠ Mloc(A). © 2008 University of Houston.
|Journal||Houston Journal of Mathematics|
|Publication status||Published - 18 Nov 2008|
- Completely bounded module homomorphism
- Hilbert C*-module
- Injective envelope
- Local multiplier algebra
- Maximal C*-algebra of quotients