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# Journal of Operator Theory

Volume 65, Issue 1, Winter 2011  pp. 47-70.

Summary:  In analogy with the $C^*$-algebra theory, we study variants appropriate to nonselfadjoint algebras of nuclearity, the local lifting property, exactness, and the weak expectation property. In addition, we study the relationships between these notions, and how they are connected with the classical $C^*$-algebra theory through the use of $C^*$-algebras generated by the algebra.