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Journals and Conferences
A completely n -positive linear map from a locally C∗-algebra A to another locally C∗-algebra B is an n × n matrix whose elements are continuous linear maps from A to B and which verifies the condition of completely positivity. In this paper we prove a Radon-Nikodym type theorem for strict completely n-positive linear maps which describes the order relation… (More)
We will show that the bounded part of the locally C∗-algebra of all adjointable operators on the Hilbert A-module E is isomorphic to the C∗-algebra Lb(A)(b(E)) of all adjointable operators on the Hilbert b(A)-module b(E).
Let A and B be two Fréchet locally C∗-algebras, let E be a full Hilbert A-module, and let F be a Hilbert B-module. We show that a bijective linear map Φ : E → F is a unitary operator from E to F if and only if there is a map φ : A → B with closed range such that Φ (ξa) = Φ (ξ) φ (a) and φ (〈ξ, η〉) = 〈Φ(ξ) , Φ(η)〉 for all a ∈ A and for all ξ, η ∈ E. AMS… (More)
Let A be a locally C-algebra and let E be a Hilbert A-module. We show that the algebra BA(E) of all bounded A-module maps on E is a locally m-convex algebra which is algebraically and topologically isomorphic to LM(KA(E)), the algebra of all left multipliers of KA(E), where KA(E) is the locally C -algebra of all ”compact“ A-module maps on E. Also we show… (More)
The crossed products of locally C-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C-algebra is proved. 2000 AMS Mathematics subject classification. Primary 46L05, 46L55.
In this paper we study the unitary equivalence between Hilbert modules over a locally C∗-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C∗-algebra and show that a Hilbert module over a Fréchet locally C∗-algebra is countably generated if and only if the locally C∗-algebra of all ”compact” operators… (More)
In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C∗-algebra and the relationship between the set of all adjointable operators from a Hilbert A -module E to a Hilbert A module F and the set of all adjointable operators from the multiplier module M(E) of E to the multiplier module M(F ) of F.
We introduce the notion of strong Morita equivalence for group actions on locally C-algebras and prove that the crossed products associated with two strongly Morita equivalent continuous inverse limit actions of a locally compact group G on the locally C∗-algebras A and B are strongly Morita equivalent. This generalizes a result of F. Combes, Proc. London… (More)
In this paper we introduce the notion of linking algebra of a Hilbert module over a locally C -algebra and we extend in the context of locally C -algebras a result of Brown, Green and Rie¤el [Paci c J.,1977] which states that two C -algebras are strongly Morita equivalent if and only if they are isomorphic with two complementary full corners of a C… (More)
We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel’fand,Naimark,Segal) construction for completely positive linear maps between locally C-algebras. As an application of this construction, we show that a covariant completely positive linear map ρ from a locally C-algebra A to another locally C -algebra B with respect to a locally… (More)