α-COMPLETELY POSITIVE MAPS ON LOCALLY C -ALGEBRAS, KREIN MODULES AND RADON-NIKODÝM THEOREM

In this paper, we study α-completely positive maps between locally C*-algebras. As a generalization of a completely positive map, an α-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 represent...

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Veröffentlicht in:Journal of the Korean Mathematical Society 2013, 50(1), , pp.61-80
Hauptverfasser: Heo, Jaeseong, Ji, Un Cig, Kim, Young Yi
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Sprache:eng
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Zusammenfassung:In this paper, we study α-completely positive maps between locally C*-algebras. As a generalization of a completely positive map, an α-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 α-completely positive map of a locally C*-algebra on a Krein locally C*-module. Using this construction, we establish the Radon-Nikodym type theorem for α-completely positive maps on locally C*-algebras. As an application, we study an extremal problem in the partially ordered cone of α-completely positive maps on a locally C*-algebra. KCI Citation Count: 5
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2013.50.1.061