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KSGNS type construction for $\alpha $-completely positive maps on Krein $C^{\ast}$-modules
- Source :
- Complex Anal. Oper. Theory 10 (2016), no. 3, 617-638
- Publication Year :
- 2014
-
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.<br />Comment: 20 pages, to appear in Complex Analysis Operator Theory
Details
- Database :
- arXiv
- Journal :
- Complex Anal. Oper. Theory 10 (2016), no. 3, 617-638
- Publication Type :
- Report
- Accession number :
- edsarx.1404.5238
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s11785-015-0520-5