Noncommutative Kernels
| dc.contributor.author | Marx, Gregory | en |
| dc.contributor.committeechair | Ball, Joseph A. | en |
| dc.contributor.committeemember | Rossi, John F. | en |
| dc.contributor.committeemember | Floyd, William J. | en |
| dc.contributor.committeemember | Elgart, Alexander | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2017-07-18T08:00:37Z | en |
| dc.date.available | 2017-07-18T08:00:37Z | en |
| dc.date.issued | 2017-07-17 | en |
| dc.description.abstract | Positive 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 |
| dc.description.degree | Ph. D. | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:12415 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/78353 | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Noncommutative kernels | en |
| dc.subject | noncommutative functions | en |
| dc.subject | uniformly bounded kernels | en |
| dc.subject | completely positive kernels | en |
| dc.subject | completely positive maps | en |
| dc.subject | completely bounded maps | en |
| dc.subject | Hilbert C*-modules | en |
| dc.subject | Hilbert W*-modules | en |
| dc.title | Noncommutative Kernels | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Ph. D. | en |
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