Browsing by Subject "Hilbert locally C*-module"

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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.