Browsing by Subject "completely positive map"

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    A note on Radon-Nikodym derivatives and similarity for completely bounded maps
    (Wydawnictwo A G H, 2009) Gheondea, A.; Kavruk, A. Ş.
    We point out a relation between the Arveson’s Radon-Nikodým derivative and known similarity results for completely bounded maps. We also consider Jordan type decompositions coming out from Wittstock’s Decomposition Theorem and illustrate, by an example, the nonuniqueness of these decompositions.
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    Operator models for hilbert locally c*-modules
    (Element D.O.O., 2017) Gheondea, A.
    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 Hilbert locally C*-modules and, as an application, we obtain a direct construction of the exterior tensor product of Hilbert locally C*-modules. These are obtained as consequences of a general dilation theorem for positive semidefinite kernels invariant under an action of a ∗-semigroup with values locally bounded operators. As a by-product, we obtain two Stinespring type theorems for completely positive maps on locally C*-algebras and with values locally bounded operators. © 2017, Element D.O.O. All rights reserved.