Noncommutative Kernels

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2017

Author dc:creator

• Marx, Gregory

Chair dc:contributor.committeechair

• Ball, Joseph A.

Committee members dc:contributor.committeemember

• Rossi, John F.
• Floyd, William J.
• Elgart, Alexander

• Noncommutative kernels
• noncommutative functions
• uniformly bounded kernels
• completely positive kernels
• completely positive maps
• completely bounded maps
• Hilbert C*-modules
• Hilbert W*-modules

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:12415

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/78353