Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 99-113.

Abelian strict approximation in multiplier

$C^*$ -algebras and related questions

Authors: Claudio D'Antoni (1) and Laszlo Zsido (2)
Author institution: (1) Dipartimento di Matematica, Universita di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italia

Summary: We prove a general result on the strict approximability of normal elements of the multiplier algebra

$M(A)$ of a

$\sigma$ -unital

$C^*$ -algebra

$A$ from commutative

$C^*$ -algebras of

$A$ . As an application, we reprove a result of L.G. Brown concerning the non-existence of non-zero separable hereditary

$C^*$ -algebras of the corona algebras of

$\sigma$ -unital

$C^*$ -algebras. Subsequently we characterize the situation in which an

$W^*$ -algebras (whose class contains all corona algebras of

$\sigma$ -unital

$C^*$ -algebras) allows non-zero separable hereditary

$C^*$ -subalgebras.

Contents Full-Text PDF