Operator models for hilbert locally c*-modules

Date
2017
Authors
Gheondea, A.
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Instructor
Source Title
Operators and matrices
Print ISSN
1846-3886
Electronic ISSN
Publisher
Element D.O.O.
Volume
11
Issue
3
Pages
639 - 667
Language
English
Type
Article
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Abstract

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.

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Keywords
Projective limit, Primary 47A20, Secondary 46L89, 46E22, 43A35, Locally Hilbert space, inductive limit, Locally C*-algebra, Hilbert locally C*-module, Positive semidefinite kernel, *-semigroup, invariant kernel, completely positive map, Reproducing kernel
Citation
Published Version (Please cite this version)