KSGNS Type Constructions for alpha-Completely Positive Maps on Krein C*-Modules

摘要

In this paper, we investigate Phi-maps associated to a certain type of alpha-completely positive maps. We then prove a Kasparov-Stinespring-Gel'fand-Naimark-Segal (KSGNS) type theorem for alpha-completely positive maps on Krein C*-modules and show that the minimal KSGNS construction is unique up to unitary equivalence. We also establish a covariant version of the KSGNS type theorem for a covariant alpha-completely positive map and study the structure of minimal covariant KSGNS constructions.