Gheondea, A.2018-04-122018-04-1220171846-3886http://hdl.handle.net/11693/36991We 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.EnglishProjective limitPrimary 47A20Secondary 46L8946E2243A35Locally Hilbert spaceinductive limitLocally C*-algebraHilbert locally C*-modulePositive semidefinite kernel*-semigroupinvariant kernelcompletely positive mapReproducing kernelArticle10.7153/oam-11-43