Journal of Operator Theory

Volume 85, Issue 2, Spring 2021 pp. 505-526.

2-positive almost order zero maps and decomposition rank

Authors: Yasuhiko Sato
Author institution: Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

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

DOI: http://dx.doi.org/10.7900/jot.2019nov21.2290
Keywords: nuclear $C^*$-algebras, $2$-positive maps, order zero, decomposition rank

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