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Open projections and suprema in the Cuntz semigroup

Published online by Cambridge University Press:  27 September 2016

JOAN BOSA ,
GABRIELE TORNETTA  and
JOACHIM ZACHARIAS
JOAN BOSA
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow e-mails: joan.bosa@glasgow.ac.uk, g.tornetta.1@research.gla.ac.uk, Joachim.Zacharias@glasgow.ac.uk
GABRIELE TORNETTA
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow e-mails: joan.bosa@glasgow.ac.uk, g.tornetta.1@research.gla.ac.uk, Joachim.Zacharias@glasgow.ac.uk
JOACHIM ZACHARIAS
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow e-mails: joan.bosa@glasgow.ac.uk, g.tornetta.1@research.gla.ac.uk, Joachim.Zacharias@glasgow.ac.uk
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 1 , January 2018 , pp. 135 - 146
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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