Operator models for hilbert locally c*-modules

dc.citation.epage667en_US
dc.citation.issueNumber3en_US
dc.citation.spage639en_US
dc.citation.volumeNumber11en_US
dc.contributor.authorGheondea, A.en_US
dc.date.accessioned2018-04-12T10:59:18Z
dc.date.available2018-04-12T10:59:18Z
dc.date.issued2017en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe 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.en_US
dc.identifier.doi10.7153/oam-11-43en_US
dc.identifier.issn1846-3886
dc.identifier.urihttp://hdl.handle.net/11693/36991
dc.language.isoEnglishen_US
dc.publisherElement D.O.O.en_US
dc.relation.isversionofhttp://dx.doi.org/10.7153/oam-11-43en_US
dc.source.titleOperators and matricesen_US
dc.subjectProjective limiten_US
dc.subjectPrimary 47A20en_US
dc.subjectSecondary 46L89en_US
dc.subject46E22en_US
dc.subject43A35en_US
dc.subjectLocally Hilbert spaceen_US
dc.subjectinductive limiten_US
dc.subjectLocally C*-algebraen_US
dc.subjectHilbert locally C*-moduleen_US
dc.subjectPositive semidefinite kernelen_US
dc.subject*-semigroupen_US
dc.subjectinvariant kernelen_US
dc.subjectcompletely positive mapen_US
dc.subjectReproducing kernelen_US
dc.titleOperator models for hilbert locally c*-modulesen_US
dc.typeArticleen_US

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