The cone of functionals on the Cuntz semigroup

By Leonel Robert. 2011

56 citations recorded by the source corpus.

The functionals on an ordered semigroup S in the category Cu--a category to which the Cuntz semigroup of a C*-algebra naturally belongs--are investigated. After appending a new axiom to the category Cu, it is shown that the "realification" S_R of S has the same functionals as S and, moreover, is recovered functorially from the cone of functionals of S. Furthermore, if S has a weak Riesz decomposition property, then S_R has refinement and interpolation properties which imply that the cone of functionals on S is a complete distributive lattice. These results apply to the Cuntz semigroup of a C*-algebra. At the level of C*-algebras, the operation of realification is matched by tensoring with a certain stably projectionless C*-algebra.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1817ce167ae023ec6a43711efd49574e69c10dc3

Citations in the corpus

• C*-algebras of stable rank one and their Cuntz semigroups (2018, unknown): “By Remark 3.10, S satisfies (O6+) and hence the weaker axiom (O6) introduced in [Rob13].”