arXiv subjects
Publications and source records attributed to Maria Joita.
In this paper we consider the unbounded local completely positive and local completely contractive maps on maximal tensor product of unital locally C*-algebras and discuss on extremal points of certain convex subsets in the set of such maps.
Given two range space relations A and B in Hilbert spaces, we characterize the existence of a range space operator T such that A = BT, respectively A = TB.
In this paper, we investigate $Φ$-maps associated to a certain type of $α$-completely positive maps. We then prove a KSGNS (Kasparov--Stinespring--Gel'fand--Naimark--Segal) type theorem for $α$-completely positive maps on Krein $C^*$-modules and show that the minimal KSGNS construction is unique up to unitary equivalence. We also establish a covariant version of the KSGNS type theorem for a covariant $α$-completely positive map and study the structure of minimal covariant KSGNS constructions.
In this paper we introduce a property of ergodic flows, called Property B. We prove that any ergodic hyperfinite equiva- lence relation of type III_o whose associated flow satisfies this property is not of product type. A consequence of this result is that any properly ergodic ow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which - up to conjugacy - is a flow built under a function with the dyadic odometer as base automorphism.
In this paper we introduce a notion of Morita equivalence for Hilbert C*-modules in terms of the Morita equivalence of the algebras of compact operators on Hilbert C*-modules. We investigate some properties of the new version of Morita equivalence and obtain some results. We then applied our results to study the continuous actions of locally compact groups on full Hilbert C*-modules. We present an extension of Green's theorem in the context of Hilbert C*-modules as well.
We prove a covariant version of the Stinespring theorem for Hilbert C*-modules.
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 Math. Soc. 49(1984) and R. E. Curto, P.S. Muhly, D. P. Williams, Proc. Amer. Soc. 90(1984).
We introduce the concept of frame of multipliers in Hilbert modules over pro-C*-algebras and show that many properties of frames in Hilbert C*-modules are valid for frames of multipliers in Hilbert modules over pro-C*-algebras.
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 extend to the context of locally C*-algebras a result of F. Combes [Proc. London Math. Soc. 49(1984), 289-306].
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 L(H) and the extreme points in the set of unital completely n-positive linear maps from A to L(H) are characterized in terms of the representation induced by each completely n-positive linear map.
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 $C^{*}$-dynamical system $(G,A,α)$ extends to a completely positive linear map on the crossed product $A\times_{α^{}}G$.
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.
052 A completely $n$ -positive linear map from a locally $C^{\ast}$-algebra $A$ to another locally $C^{\ast}$-algebra $B $is an $n\times n$ 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 on the set of all strict completely $n$ -positive linear maps from a locally $C^{\ast }$-algebra $A$ to a $C^{\ast}$-algebra $B$, in terms of a self-dual Hilbert $C^{\ast}$-module structure induced by each strict completely $n$ -positive linear map. As applications of this result we characterize the pure completely $n$-positive linear maps from $A$ to $B$ and the extreme elements in the set of all identity preserving completely $n$-positive linear maps from $A$ to $B$. Also we determine a certain class of extreme elements in the set of all identity preserving completely positive linear maps from $A$ to $M_{n}(B)$.
In this paper, by analogy with the case of C*-algebras, we define the notion of induced representation of a locally C*-algebra, and then we prove a imprimitivity theorem for induced representations of locally C*-algebras.
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 Frechet locally C*-algebra is countably generated if and only if the locally C*-algebra of all ''compact'' operators has an approximate unit.