KSGNS type construction for $\alpha $-completely positive maps on Krein $C^{\ast}$-modules
Operator Algebras
2021-07-23 v2 Mathematical Physics
Functional Analysis
math.MP
Abstract
In this paper, we investigate -maps associated to a certain type of -completely positive maps. We then prove a KSGNS (Kasparov--Stinespring--Gel'fand--Naimark--Segal) type theorem for -completely positive maps on Krein -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 -completely positive map and study the structure of minimal covariant KSGNS constructions.
Cite
@article{arxiv.1404.5238,
title = {KSGNS type construction for $\alpha $-completely positive maps on Krein $C^{\ast}$-modules},
author = {Mohammad Sal Moslehian and Maria Joita and Un Cig Ji},
journal= {arXiv preprint arXiv:1404.5238},
year = {2021}
}
Comments
20 pages, to appear in Complex Analysis Operator Theory