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Journal of Operator Theory

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

Nuclearity-related properties for nonselfadjoint algebras

Authors: David P. Blecher (1) and Benton L. Duncan (2)
Author institution: (1) Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.
(2) Department of Mathematics, North Dakota State University, NDSU Department 2750 PO Box 6050, Fargo, ND 58108-6050, U.S.A.

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.

Keywords:  Nonselfadjoint operator algebras, tensor products, nuclearity, exactness, weak expectation property WEP, LLP, unique extension property, $C^*$-envelope

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