Open Projections and Suprema in the Cuntz Semigroup
Bosa, Joan · Tornetta, Gabriele · Zacharias, Joachim
Operator Algebras
Functional Analysis
46L10, 46L35 (Primary), 06F05, 19K14, 46L30, 46L80 (Secondary)
Original · EN
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.
English translation
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