Dilations of doubly invariant kernels valued in topologically ordered *- spaces

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buir.advisorGheondea E., Aurelian B. N.
dc.contributor.authorAy, Serdar
dc.date.accessioned2018-08-01T11:04:43Z
dc.date.available2018-08-01T11:04:43Z
dc.date.copyright2018-06
dc.date.issued2018-06
dc.date.submitted2018-07-17
dc.departmentDepartment of Mathematicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2018.en_US
dc.descriptionIncludes bibliographical references (leaves 102-107).en_US
dc.description.abstractAn ordered *-space Z is a complex vector space with a conjugate linear involution *, and a strict cone Z+ consisting of self adjoint elements. A topologically ordered *-space is an ordered *-space with a locally convex topology compatible with its natural ordering. A VE (Vector Euclidean) space, in the sense of Loynes, is a complex vector space equipped with an inner product taking values in an ordered *-space, and a VH (Vector Hilbert) space, in the sense of Loynes, is a VE-space with its inner product valued in a complete topologically ordered *-space and such that its induced locally convex topology is complete. On the other hand, dilation type theorems are important results that often realize a map valued in a certain space as a part of some simpler elements on a bigger space. Dilation results today are of an extraordinary large diversity and it is a natural question whether most of them can be uni*ed under general theorems. We study dilations of weakly positive semide*nite kernels valued in (topologically) ordered *-spaces, which are invariant under left actions of *-semigroups and right actions of semigroups, called doubly invariant. We obtain VE and VHspaces linearisations of such kernels, and on equal foot, their reproducing kernel spaces, and operator representations of the acting semigroups. The main results are used to unify many of the known dilation theorems for invariant positive semide*nite kernels with operator values, also for kernels valued in certain algebras, as well as to obtain some new dilation type results, in the context of Hilbert C*-modules, locally Hilbert C*-modules and VH-spaces.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityby Serdar Ay.en_US
dc.embargo.release2019-07-17
dc.format.extentvii, 107 leaves ; 30 cmen_US
dc.identifier.itemidB158692
dc.identifier.urihttp://hdl.handle.net/11693/47709
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectTopologically Ordered *-Spaceen_US
dc.subjectVE-Spaceen_US
dc.subjectVH-Spaceen_US
dc.subjectHermitian Kernelen_US
dc.subjectWeakly Positive Semide nite Kernelen_US
dc.subjectDoubly Invariant Kernelen_US
dc.subjectLinearisationen_US
dc.subjectReproducing Kernelen_US
dc.subject*-representationen_US
dc.subjectCompletely Positive Mapen_US
dc.titleDilations of doubly invariant kernels valued in topologically ordered *- spacesen_US
dc.title.alternativeSıralı *-Uzayı değerli çift değişmez çekirdeklerin genleşmesien_US
dc.typeThesisen_US

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