2-positive almost order zero maps and decomposition rank

2019/08/09 by Yasuhiko Sato, Sato, Yasuhiko · 1 citation
Mathematics · #46L05 #46L35 #46L45 #81P70 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1908.03466

openalex publication_date 2019/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider 2-positive almost order zero (disjointness preserving) maps on C*-algebras. Generalizing the argument of M. Choi for multiplicative domains, we give an internal characterization of almost order zero for 2-positive maps. It is also shown that complete positivity can be reduced to 2-positivity in the definition of decomposition rank for unital separable C*-algebras.

Citations

• Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary

Cited by

• Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem

Related

• Completely positive maps of order zero
• Images of Order Zero Maps
• A minimal completion theorem and almost everywhere equivalence for Completely Positive maps
• Approximately order zero maps between C*-algebras
• Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank