THE CUNTZ SEMIGROUP AND COMPARISON OF OPEN PROJECTIONS

By E. Ortega, M. Rørdam, Hannes Thiel. 2010

67 citations recorded by the source corpus.

Abstract We show that a number of naturally occurring comparison relations on positive elements in a C ⁎ -algebra are equivalent to natural comparison properties of their corresponding open projections in the bidual of the C ⁎ -algebra. In particular we show that Cuntz comparison of positive elements corresponds to a comparison relation on open projections, that we call Cuntz comparison, and which is defined in terms of—and is weaker than—a comparison notion defined by Peligrad and Zsido. The latter corresponds to a well-known comparison relation on positive elements defined by Blackadar. We show that Murray–von Neumann comparison of open projections corresponds to tracial comparison of the corresponding positive elements of the C ⁎ -algebra. We use these findings to give a new picture of the Cuntz semigroup.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a12fb8f6dacbc924a569ed0eb34e3999eefcd6c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ramon Antoine
2. Hannes Thiel
3. F. Perera
4. W. Winter
5. Leonel Robert
6. Andrew S. Toms

In Mathematical Physics

1. Ramon Antoine
2. Hannes Thiel
3. F. Perera
4. W. Winter
5. Leonel Robert
6. Andrew S. Toms

Citations in the corpus

• Tensor products and regularity properties of Cuntz semigroups (2014, background): “[70] Ortega, Eduard; Rørdam, Mikael; Thiel, Hannes, The Cuntz semigroup and comparison of open projections, J.”
• C*-algebras of stable rank one and their Cuntz semigroups (2018, unknown): “For a fuller account, we refer the reader to [APT11], [ORT11], [APT18], and the references therein.”