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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