Images of Order Zero Maps

2023/12/13 by Courtney, Kristin, Winter, Wilhelm
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2312.08215

Abstract

We give sufficient conditions allowing one to build a C*-algebraic structure on a self-adjoint linear subspace of a C*-algebra in such a way that the subspace is naturally identified with the resulting C*-algebra via a completely positive order zero map. This leads to necessary and sufficient conditions to realize a self-adjoint linear subspace of a C*-algebra as the image of an order zero map from a C*-algebra and to determine whether it is completely order isomorphic to a C*-algebra via an order zero map.

Related

• Completely positive maps of order zero
• Approximately order zero maps between C*-algebras
• Maps preserving the diamond partial order
• 2-positive almost order zero maps and decomposition rank
• Linear maps preserving regularity in C∗-algebras