Open projections and suprema in the Cuntz semigroup

Bosa, J., Tornetta, G. and Zacharias, J. (2018) Open projections and suprema in the Cuntz semigroup. Mathematical Proceedings of the Cambridge Philosophical Society, 164(1), pp. 135-146. (doi:10.1017/S030500411600089X)

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Abstract

We provide a new and concise proof of the existence of suprema in the Cuntz semigroup using the open projection picture of the Cuntz semigroup initiated in [12]. Our argument is based on the observation that the supremum of a countable set of open projections in the bidual of a C*-algebra A is again open and corresponds to the generated hereditary C*-subalgebra of A.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Tornetta, Mr Gabriele and Bosa, Dr Joan and Zacharias, Dr Joachim
Authors: Bosa, J., Tornetta, G., and Zacharias, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Proceedings of the Cambridge Philosophical Society
Publisher:Cambridge University Press
ISSN:0305-0041
ISSN (Online):1469-8064
Published Online:27 September 2016
Copyright Holders:Copyright © 2016 Cambridge Philosophical Society
First Published:First published in Mathematical Proceedings of the Cambridge Philosophical Society 164(1):135-146
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
626331The Cuntz Semigroup and the Fine Stucture of Nuclear C*-AlgebrasJoachim ZachariasEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/2M&S - MATHEMATICS