Characterization of the order relation on the set of completely -positive linear maps between -algebras.
Commutants of von Neumann correspondences and duality of Eilenberg-Watts theorems by Rieffel and by Blecher
The category of von Neumann correspondences from 𝓑 to 𝓒 (or von Neumann 𝓑-𝓒-modules) is dual to the category of von Neumann correspondences from 𝓒' to 𝓑' via a functor that generalizes naturally the functor that sends a von Neumann algebra to its commutant and back. We show that under this duality, called commutant, Rieffel's Eilenberg-Watts theorem (on functors between the categories of representations of two von Neumann algebras) switches into Blecher's Eilenberg-Watts theorem (on functors...
Completely multi-positive linear maps between locally C*-algebras and representations on Hilbert modules
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.
Continuous -frame in Hilbert -modules.
Covariant version of the Stinespring type theorem for Hilbert C*-modules
In this paper, we prove a covariant version of the Stinespring theorem for Hilbert C*-modules. Also, we show that there is a bijective correspondence between operator valued completely positive maps, (u′, u)-covariant with respect to the dynamical system (G, η, X) on Hilbert C*-modules and (u′, u)-covariant operator valued completely positive maps on the crossed product G ×η X of X by η.
Crossed products by Hilbert pro-C*-bimodules
We define the crossed product of a pro-C*-algebra A by a Hilbert A-A pro-C*-bimodule and we show that it can be realized as an inverse limit of crossed products of C*-algebras by Hilbert C*-bimodules. We also prove that under some conditions the crossed products of two Hilbert pro-C*-bimodules over strongly Morita equivalent pro-C*-algebras are strongly Morita equivalent.