α-completely positive maps on locally C*-algebras, Krein modules and Radon-Nikodym theorem
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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.
Abstract
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.
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