Krein Space Representations and Radon–Nikodým Theorem for Local α -Completely Positive Maps

Abstract

In this paper, we prove a Krein space J-representation theorem for local alpha-completely positive maps on locally C*-algebras. Using this representation, we construct a Krein space J-representation associated with a pair of two maps (phi, Phi) where phi is a local alpha-completely positive map on a locally C*-algebra and Phi is a phi-map. Also, we discuss the minimality of Krein space J-representations, and as an application, we establish the Radon-Nikodym theorem for local alpha-completely positive maps.