New York Journal of Mathematics
Volume 27 (2021), 918-922


Cristian Ivanescu and Dan Kucerovsky

Cu-nuclearity implies LLP and exactness

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Published: June 17, 2021.
Keywords: C*-algebra, nuclearity.
Subject: Primary 46A32, 46L06, Secondary 47L07, 47L50.

The Cu-nuclearity property is an analogue of Skandalis's notion of K-nuclearity, adapted to the case of Cuntz semigroups of C*-algebras. We prove that this implies nuclearity, and we introduce a weaker form of the condition. We prove that the new condition weak Cu-nuclearity, for simple separable C*-algebras, implies exactness and the local lifting property (LLP). We also prove that if A is a simple C*-algebra with the weak Cu-nuclearity property, and B is any simple C*-algebra, then A ⊗min B = A ⊗max B. We prove that Cu-nuclearity does imply nuclearity, and that in some cases this is also true for weak Cu-nuclearity.


The second-named authour thanks NSERC for financial support.

Author information

Cristian Ivanescu:
Department of Mathematics and Statistics
Grant MacEwan University
Edmonton, Alberta, T5J 4S2, Canada


Dan Kucerovsky:
Department of Mathematics and Statistics
University of New Brunswick
Fredericton, New Brunswick, E3B 5A3, Canada