Much of operator theory hangs its coat on the spectral theorem, but the latter is exclusive to normal operators. Likewise, isometries are well understood via the Wold decomposition. It is von Neumann's inequality that enables a functional calculus for arbitrary contractions on Hilbert spaces. There are essentially two avenues that lead to von Neumann, one being the analytical theory of positive maps, the other marked by geometric dilation theorems. These diverse lines of approach are in fact unified by the inequality. Although our main focus is von Neumann's inequality, for which we provide four different proofs, we shall, however, periodically indulge in some of its intricate cousins.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.100204 |
| Date | January 2007 |
| Creators | Rainone, Timothy. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Mathematics and Statistics.) |
| Rights | © Timothy Rainone, 2007 |
| Relation | alephsysno: 002666401, proquestno: AAIMR38429, Theses scanned by UMI/ProQuest. |
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