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. / Ph. D.
Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/78353 |
Date | 17 July 2017 |
Creators | Marx, Gregory |
Contributors | Mathematics, Ball, Joseph A., Rossi, John F., Floyd, William J., Elgart, Alexander |
Publisher | Virginia Tech |
Source Sets | Virginia Tech Theses and Dissertation |
Detected Language | English |
Type | Dissertation |
Format | ETD, application/pdf |
Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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