Journal of Operator Theory

Volume 50, Issue 2, Fall 2003 pp. 263-281.

LB algebras

Authors: Cornel Pasnicu
Author institution: Department of Mathematics and Computer Science, University of Puerto Rico, Box 23355, San Juan, PR 00931-3355, USA

Summary: We introduce some classes of

$C^*$ -algebras with ``good" local approximation properties --- the class of

$\LB$ algebras and several subclasses of it --- which generalize, among others, the

$\AH$ algebras, the

$\AD$ algebras and the separable, simple

$C^*$ -algebras with an approximate unit of projections. We initiate the study of these new and rich classes of

$C^*$ -algebras, proving results about the ideal property, real rank zero, the projection property, ideal structure, inductive limits, stable isomorphism, hereditary

$C^*$ -subalgebras and extensions. Some of our previous results about

$\AH$ algebras and

$\GAH$ algebras are generalized.

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