engleski

The local multiplier algebra of a C*-algebra with finite dimensional irreducible representations

We describe, up to isomorphism, the local multiplier algebra $M_{; ; ; loc}; ; ; (A)$ of a $C^*$-algebra $A$ which admits only finite dimensional irreducible representations: $M_{; ; ; loc}; ; ; (A)$ in this case is a finite or countable direct product of $C^*$-algebras of the form $C(X_n)\otimes M_n$, where each space $X_n$ is Stonean. In particular, $M_{; ; ; loc}; ; ; (A)$ is an $AW^*$-algebra of type I, so it admits only inner derivations and it coincides with the injective envelope $I(A)$ of $A$.

C*-algebra ; finite dimensional irreducible representation ; local multiplier algebra ; derivation

nije evidentirano