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In this article, we introduce local completely positive $k$-linear maps between locally $C^{\ast}$-algebras and obtain Stinespring type representation by adopting the notion of "invariance" defined by J. Heo for $k$-linear maps between…

Operator Algebras · Mathematics 2021-10-01 Anindya Ghatak , Santhosh Kumar Pamula

We introduce an equivalence relation on the set of all completely positive maps between Hilbert modules over pro-C*-algebras and analyze the Stinespring's construction for equivalent completely positive maps. We then give a preorder…

Operator Algebras · Mathematics 2025-05-21 Bhumi Amin , Ramesh Golla

In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert $A$-modules over locally $C^{*}$-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring…

Operator Algebras · Mathematics 2021-07-23 M. S. Moslehian , A. Kusraev , M. Pliev

We derive Paschke's GNS construction for completely positive maps on unital pro-C*-algebras from the KSGNS construction, presented by M. Joita [J. London Math. Soc. {\bf 66} (2002), 421--432], and then we deduce an analogue of Stinespring…

Operator Algebras · Mathematics 2017-01-05 Khadijeh Karimi , Kamran Sharifi

The aim of this article is to extend the results of Asadi M.B, B.V.R. Bhat, G. Ramesh, K. Sumesh about completely positive maps on Hilbert C*-modules. We prove a Stinespring type theorem for a finite family of completely positive maps on…

Operator Algebras · Mathematics 2012-10-23 Marat Pliev

In this article, we investigate certain basic properties of invariant multilinear CP maps. For instance, we prove Russo-Dye type theorem for invariant multilinear positive maps on both commutative $C^*$-algebras and finite-dimensional…

Operator Algebras · Mathematics 2024-01-10 Anindya Ghatak , Aryaman Sensarma

Given a completely positive (CP) map $T$, there is a theorem of the Radon-Nikodym type [W.B. Arveson, Acta Math. {\bf 123}, 141 (1969); V.P. Belavkin and P. Staszewski, Rep. Math. Phys. {\bf 24}, 49 (1986)] that completely characterizes all…

Mathematical Physics · Physics 2007-05-23 Maxim Raginsky

052<p type="texpara" tag="Body Text" et="abstract" >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…

Operator Algebras · Mathematics 2007-05-23 Maria Joita

Motivated by Cuntz-Krieger-Toeplitz systems associated to undirected graphs and representations of groupoids, we obtain a generalisation of the Sz-Nagy's Dilation Theorem for operator valued partially positive semidefinite maps on…

Operator Algebras · Mathematics 2025-11-04 Aurelian Gheondea , Bogdan Udrea

We introduce completely semi-$\varphi$-maps on Hilbert $C^*$-modules as a generalization of $\varphi$-maps. This class of maps provides examples of CP-extendable maps which are not CP-H-extendable, in Skeide-Sumesh's sense. Using the…

Operator Algebras · Mathematics 2016-08-02 Mohammad B. Asadi , Reza Behmani , Ali R. Medghalchi , Hamed Nikpey

We single out the concept of concrete Hilbert module over a locally $C^*$-algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Using this concept, we construct an operator model for all…

Operator Algebras · Mathematics 2025-11-04 Aurelian Gheondea

We strengthen Mohammad B. Asadi's analogue of Stinespring's theorem for certain maps on Hilbert C*-modules. We also show that any two minimal Stinespring representations are unitarily equivalent. We illustrate the main theorem with an…

Operator Algebras · Mathematics 2014-05-16 B V Rajarama Bhat , G. Ramesh , K. Sumesh

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…

Operator Algebras · Mathematics 2007-05-23 Maria Joita

We show that an operator valued $\alpha$-completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define…

Operator Algebras · Mathematics 2013-08-08 Maria Joiţa

A completely positive linear map $\varphi$ from a C*-algebra $A$ into $B(H)$ has a Stinespring representation as $\varphi(a) = X^*\pi(a)X,$ where $\pi$ is a *-representation of $A$ on a Hilbert space $K$ and $X$ is a bounded operator from…

Operator Algebras · Mathematics 2021-08-27 Erik Christensen

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of…

Mathematical Physics · Physics 2009-04-07 F. Bagarello , A. Inoue , C. Trapani

We introduce a preorder relation in the collection of all operator valued completely positive maps on a full Hilbert C*-module and characterize this relation in terms of the Stinespring construction associated to each completely positive…

Operator Algebras · Mathematics 2018-06-18 Maria Joiţa

We prove a local convex version of Arveson's extension theorem and of Wittstock's extension theorem. Also we prove a Stinespring type theorem for unbounded local completely contractive maps.

Operator Algebras · Mathematics 2022-02-11 Maria Joiţa

The Radon-Nikodym formalism is used to study the structure of the set of positive maps from $\mathcal{B}(\mathcal{H})$ into itself, where $\mathcal{H}$ is a finite dimensional Hilbert space. In particular, this formalism was employed to…

Operator Algebras · Mathematics 2017-07-06 W. A. Majewski

We develop a Kubo--Ando theory on order intervals of completely positive maps. Using Arveson's Radon--Nikodym theorem as a structural tool, we define relative Kubo--Ando means \(\Phi\sigma_\Omega\Psi\) for completely positive maps dominated…

Operator Algebras · Mathematics 2026-05-19 Mohsen Kian
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