 

Cristian Ivanescu and
Dan Kucerovsky
Cunuclearity implies LLP and exactness
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Published: 
June 17, 2021. 
Keywords: 
C*algebra, nuclearity. 
Subject: 
Primary 46A32, 46L06, Secondary 47L07, 47L50. 


Abstract
The Cunuclearity property is an analogue of Skandalis's notion of Knuclearity, 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 Cunuclearity, 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 Cunuclearity property, and B is any simple C*algebra, then A ⊗_{min} B = A ⊗_{max} B. We prove that Cunuclearity does imply nuclearity, and that in some cases this is also true for weak Cunuclearity.


Acknowledgements
The secondnamed authour thanks NSERC for financial support.


Author information
Cristian Ivanescu:
Department of Mathematics and Statistics
Grant MacEwan University
Edmonton, Alberta, T5J 4S2, Canada
ivanescuc@macewan.ca
Dan Kucerovsky:
Department of Mathematics and Statistics
University of New Brunswick
Fredericton, New Brunswick, E3B 5A3, Canada
dkucerov@unb.ca

