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.

Keywords: $C^*$-algebra, $\LB$ algebra, special $\LB$ algebra, ultraspecial $\LB$ algebra, the ideal property, the projection property, real rank zero, inductive limits, Riesz decomposition property, ideal generated by projections, stable isomorphism, hereditary $C^*$-subalgebra, extension of two $C^*$-algebras

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