Browsing by Subject "Locally Hilbert space"

Now showing 1 - 3 of 3

Open Access
On locally Hilbert spaces
(AGH University of Science and Technology Press, 2016) Gheondea, A.
This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their subspaces, linear functionals and dual spaces. Keywords: locally Hilbert space, inductive limit, projective limit, orthocomplemented subspaces, linear functional, dual spaces. © AGH University of Science and Technology Press, 2016.
Open Access
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.
Open Access
The spectral theorem for locally normal operators
(AGH University of Science and Technology, 2018) Gheondea, Aurelian
We prove the spectral theorem for locally normal operators in terms of a locally spectral measure. In order to do this, we first obtain some characterisations of local projections and we single out and investigate the concept of a locally spectral measure.