The Pedersen ideal and the representation of \(C^*\)-algebras (Q1058707)

Let A be a \(C^*\)-algebra and let K(A) be the Pedersen ideal of A (i.e., the minimal dense, order related, ideal in A). Let Z be the center of A and assume throughout that ZA is dense in A. Then the author shows that \(K(A)=K(Z)A=(K(A)\cap Z)A\). \textit{K. H. Hofman} [Bull. Am. Math. Soc. 78, 291-373 (1972; Zbl 0237.16018)] has shown that A is isometric *- isomorphic to a \(C^*\)-bundle of sections vanishing at \(\infty\) over the carrier space of Z. The author proves that K(A) is mapped by this isometric isomorphism onto the sections with compact support while the multiplier algebra of K(A) is isometric isomorphic to the \(C^*\)-algebra of all bounded sections over the carrier space.