A KSGNS (Kasparov, Stinespring, Gel'fand, Naimark, Segal) type construction for strict (respectively, covariant non-degenerate) completely multi-positive linear maps between locally C*-algebras is described.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-5, author = {Maria Joi\c ta}, title = {Completely multi-positive linear maps between locally C*-algebras and representations on Hilbert modules}, journal = {Studia Mathematica}, volume = {173}, year = {2006}, pages = {181-196}, zbl = {1101.46039}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-5} }
Maria Joiţa. Completely multi-positive linear maps between locally C*-algebras and representations on Hilbert modules. Studia Mathematica, Tome 173 (2006) pp. 181-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-2-5/