TY - JOUR
T1 - 2-Positive Almost Order Zero Maps and Decomposition Rank
AU - Sato, Yasuhiko
N1 - Funding Information:
Acknowledgements. The author would like to thank Professor Marius Da˘dârlat for helpful comments on this research, and Professor Narutaka Ozawa for showing him the valuable survey [28]. He also expresses his gratitude to Professor Huaxin Lin and the organizers of Special Week on Operator Algebras 2019 for their kind hospitality during the author’s stay in East China Normal University. This work was supported in part by the Grant-in-Aid for Young Scientists (B) 15K17553, JSPS.
Publisher Copyright:
© Copyright by THETA, 2021
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
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U2 - 10.7900/jot.2019nov21.2290
DO - 10.7900/jot.2019nov21.2290
M3 - Article
AN - SCOPUS:85105080927
SN - 0379-4024
VL - 85
SP - 505
EP - 526
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -