The structure of invariant α-CP multilinear maps and associated J-representations
- Authors
- Heo, Jaeseong
- Issue Date
- Jul-2016
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- alpha-completely positive map; invariant multilinear map; Krein space; J -representation; Radon-Nikodym theorem; extreme point; C*-dynamical system; covariant multilinear map
- Citation
- LINEAR & MULTILINEAR ALGEBRA, v.64, no.7, pp.1295 - 1313
- Indexed
- SCIE
SCOPUS
- Journal Title
- LINEAR & MULTILINEAR ALGEBRA
- Volume
- 64
- Number
- 7
- Start Page
- 1295
- End Page
- 1313
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/154287
- DOI
- 10.1080/03081087.2015.1082963
- ISSN
- 0308-1087
- Abstract
- In this paper, we introduce a notion of alpha-completely positive multilinear maps as a generalization of completely positive multilinear maps. We construct a Krein space representation associated with an invariant alpha-completely positive multilinear map and show that the natural ordering of invariant alpha-completely positive multilinear maps is characterized in terms of the Radon-Nikodym derivatives. Finally, we construct a covariant Krein space representation associated with covariant and invariant alpha-completely positive multilinear maps and show that a covariant and invariant alpha-completely positive multilinear map on C*-algebras can be extended to an alpha-completely positive multilinear map on C*-crossed products.
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