Maximal C*-algebras of quotients and injective envelopes of C*-algebras

Details Maximal C*-algebras of quotients and injective envelopes of C*-algebras Maximal C*-algebras of quotients and injective envelopes of C*-algebras

2007-04-27

arxiv.org/abs/0704.3711v1

Mathematics

Operator Algebras

37 pages

Scientific paper

A new C*-enlargement of a C*-algebra $A$ nested between the local multiplier algebra $M_{\text{loc}}(A)$ of $A$ and its injective envelope $I(A)$ is introduced. Various aspects of this maximal C*-algebra of quotients, $Q_{\text{max}}(A)$, 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 $M_{\text{loc}}(M_{\text{loc}}(A))\ne M_{\text{loc}}(A)$.

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