Open Projections and Suprema in the Cuntz Semigroup
Operator Algebras
2015-08-31 v3 Functional Analysis
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 by Ortega, Rordam and Thiel. 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 sub-C*-algebra of A.
Cite
@article{arxiv.1411.5619,
title = {Open Projections and Suprema in the Cuntz Semigroup},
author = {Joan Bosa and Gabriele Tornetta and Joachim Zacharias},
journal= {arXiv preprint arXiv:1411.5619},
year = {2015}
}
Comments
11 pages; we fixed a gap in one of the lemmas of the previous version