Open projections and suprema in the Cuntz semigroup

Abstract

AbstractWe 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*-algebraAis again open and corresponds to the generated hereditary C*-subalgebra ofA.