Title : ( KSGNS type constructions for α-completely positive maps on Krein C-modules )
Authors: Mohammad Sal Moslehian , Maria Joita , Un Cig Ji ,
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Abstract
In this paper, we investigate $\Phi$-maps associated to a certain type of $\alpha$-completely positive maps. We then prove a KSGNS (Kasparov--Stinespring--Gel'fand--Naimark--Segal) 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.
Keywords
, KSGNS type construction; $C^*$, algebra; Hilbert $C^*$, module; $\alpha$, completely positive map; Stinespring type theorem
@article{paperid:1053154,
author = {Sal Moslehian, Mohammad and Maria Joita and Un Cig Ji},
title = {KSGNS type constructions for α-completely positive maps on Krein C-modules},
journal = {Complex Analysis and Operator Theory},
year = {2016},
volume = {10},
number = {3},
month = {September},
issn = {1661-8254},
pages = {617--638},
numpages = {21},
keywords = {KSGNS type construction; $C^*$-algebra; Hilbert $C^*$-module; $\alpha$-completely positive map; Stinespring type theorem},
}
%0 Journal Article
%T KSGNS type constructions for α-completely positive maps on Krein C-modules
%A Sal Moslehian, Mohammad
%A Maria Joita
%A Un Cig Ji
%J Complex Analysis and Operator Theory
%@ 1661-8254
%D 2016
