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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)
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… (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. 1 Introduction Locally C *-algebras are generalizations of C *-algebras. Instead of being given by a single C *-norm, the topology on a locally C *-algebra is defined by a directed… (More)
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 "… (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-algebra.
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.
The order relation on the set of completely n-positive linear maps from a pro-C *-algebra A to L(H), the C *-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive linear map. Also, the pure elements in the set of all completely n-positive linear maps from A to… (More)
In this paper, we prove that two continuous inverse limit actions α and β of a locally compact group G on the locally C *-algebras A and B are strongly Morita equivalent if and only if there is a locally C *-algebra C such that A and B appear as two complementary full corners of C and there is a continuous action γ of G on C which leaves A and B invariant… (More)