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dc.contributor.authorMarx, Gregoryen_US
dc.date.accessioned2017-07-18T08:00:37Z
dc.date.available2017-07-18T08:00:37Z
dc.date.issued2017-07-17en_US
dc.identifier.othervt_gsexam:12415en_US
dc.identifier.urihttp://hdl.handle.net/10919/78353
dc.description.abstractPositive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative kernels in the setting of Hilbert C*-modules and Hilbert W*-modules. We prove an Arveson-type extension theorem for completely positive noncommutative kernels, and we show that a uniformly bounded noncommutative kernel can be decomposed into a linear combination of completely positive noncommutative kernels.en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectNoncommutative kernelsen_US
dc.subjectnoncommutative functionsen_US
dc.subjectuniformly bounded kernelsen_US
dc.subjectcompletely positive kernelsen_US
dc.subjectcompletely positive mapsen_US
dc.subjectcompletely bounded mapsen_US
dc.subjectHilbert C*-modulesen_US
dc.subjectHilbert W*-modulesen_US
dc.titleNoncommutative Kernelsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairBall, Joseph A.en_US
dc.contributor.committeememberRossi, John F.en_US
dc.contributor.committeememberFloyd, William J.en_US
dc.contributor.committeememberElgart, Alexanderen_US


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