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α-COMPLETELY POSITIVE MAPS ON LOCALLY C*-ALGEBRAS, KREIN MODULES AND RADON-NIKODÝM THEOREM
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 Title & Authors
α-COMPLETELY POSITIVE MAPS ON LOCALLY C*-ALGEBRAS, KREIN MODULES AND RADON-NIKODÝM THEOREM
Heo, Jaeseong; Ji, Un Cig; Kim, Young Yi;
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 Abstract
In this paper, we study -completely positive maps between locally -algebras. As a generalization of a completely positive map, an -completely positive map produces a Krein space with indefinite metric, which is useful for the study of massless or gauge fields. We construct a KSGNS type representation associated to an -completely positive map of a locally -algebra on a Krein locally -module. Using this construction, we establish the Radon-Nikodm type theorem for -completely positive maps on locally -algebras. As an application, we study an extremal problem in the partially ordered cone of -completely positive maps on a locally -algebra.
 Keywords
locally -algebra;Hilbert locally -module;-completely positive map;J-representation;Krein module;minimal Krein quadruple;non-commutative Radon-Nikodm theorem;
 Language
English
 Cited by
1.
-completely positive maps of group systems and Krein module representations, Journal of Mathematical Analysis and Applications, 2014, 409, 1, 544  crossref(new windwow)
2.
The structure of invariant α-CP multilinear maps and associatedJ-representations, Linear and Multilinear Algebra, 2016, 64, 7, 1295  crossref(new windwow)
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