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A CHARACTERISATION OF TRACIALLY NUCLEAR C*-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  07 January 2019

DON HADWIN ,
WEIHUA LI Open the ORCID record for WEIHUA LI [Opens in a new window] ,
WENJING LIU  and
JUNHAO SHEN
DON HADWIN
Affiliation:
Mathematics Department, University of New Hampshire, Durham, NH 03824, USA email don@unh.edu
WEIHUA LI*
Affiliation:
Science and Mathematics Department, Columbia College Chicago, Chicago, IL 60605, USA email wli@colum.edu
WENJING LIU
Affiliation:
Mathematics Department, University of New Hampshire, Durham, NH 03824, USA email wenjingtwins87@gmail.com
JUNHAO SHEN
Affiliation:
Mathematics Department, University of New Hampshire, Durham, NH 03824, USA email Junhao.Shen@unh.edu
*
✉wli@colum.edu
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Abstract

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We give two characterisations of tracially nuclear C*-algebras. The first is that the finite summand of the second dual is hyperfinite. The second is in terms of a variant of the weak* uniqueness property. The necessary condition holds for all tracially nuclear C*-algebras. When the algebra is separable, we prove the sufficiency.

Keywords

tracially nuclearM-rank

MSC classification

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 100 , Issue 1 , August 2019 , pp. 119 - 128
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

The first three authors are, respectively, supported by a Collaboration Grant from the Simons Foundation, a Faculty Development Grant from Columbia College Chicago and a Dissertation Year Fellowship from the University of New Hampshire.

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