{"title":"2-positive almost order zero maps and decomposition rank","authors":"Yasuhiko Sato","doi":"10.7900/JOT.2019NOV21.2290","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/JOT.2019NOV21.2290","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
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.
期刊介绍：
The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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