Completely multi-positive linear maps between locally C^*-algebras and representations on Hilbert modules

Abstract

Abstract. 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.

On representations associated with completely n-positive linear maps on pro-C *-algebras

“…We say that a completely n-positive linear map [ρ ij ] n i,j=1 from A to L(H) is nondegenerate if for some approximate unit {e λ } λ∈Λ of A, the nets {ρ ii (e λ )} λ∈Λ , i = 1, 2, · · · , n, converge strictly to the identity operator on H (see [6]). …”

A Radon-Nikodým theorem for completely multi-positive linear maps and its applications

“…Besides an intrinsic interest in pro-C * -algebras as topological algebras comes from the fact that they provide an important tool in investigation of certain aspects of C * -algebras ( like multipliers of the Pedersen ideal [2,11]; tangent algebra of a C * -algebra [11]; quantum field theory [3]). In the literature, pro-C * -algebras have been given different name such as b * -algebras ( C. Apostol ), LM C * -algebras ( G. Lassner, K. Schmüdgen) or locally C * -algebras [4,6,7,8,9].…”

“…In [9], we extend the KSGNS (Kasparov, Stinespring, Gel'fend, Naimark, Segal) construction for strict completely n-positive linear maps from a pro-C * -algebra A to another pro-C * -algebra B.…”