Comparison properties of the Cuntz semigroup and applications to C*-algebras

Bosa, J. and Petzka, H. (2018) Comparison properties of the Cuntz semigroup and applications to C*-algebras. Canadian Journal of Mathematics, 70(1), pp. 26-52. (doi:10.4153/cjm-2016-049-8)

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Abstract

We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and -comparison. We show differences of all properties by providing examples, which suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bosa, Dr Joan
Authors: Bosa, J., and Petzka, H.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Canadian Journal of Mathematics
Publisher:Canadian Mathematical Society
ISSN:0008-414X
ISSN (Online):1496-4279
Published Online:25 May 2017
Copyright Holders:Copyright © 2018 Canadian Mathematical Society
First Published:First published in Canadian Journal of Mathematics 70(1): 26-52
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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