Dilation theorems for VH-spaces
| buir.advisor | Gheondea, Aurelian | |
| dc.contributor.author | Uğurcan, Barış Evren | |
| dc.date.accessioned | 2016-01-08T18:17:27Z | |
| dc.date.available | 2016-01-08T18:17:27Z | |
| dc.date.issued | 2009 | |
| dc.department | Department of Mathematics | en_US |
| dc.description | Ankara : The Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2009. | en_US |
| dc.description | Thesis (Master's) -- Bilkent University, 2009. | en_US |
| dc.description | Includes bibliographical references leaves 45-46. | en_US |
| dc.description.abstract | In the Appendix of the book Le¸cons d’analyse fonctionnelle by F. Riesz and B. Sz.-Nagy, B. Sz.-Nagy [15] proved an important theorem on operator valued positive definite maps on ∗-semigroups, which today can be considered as one of the pioneering results of dilation theory. In the same year W.F. Stinespring [11] proved another celebrated theorem about dilation of operator valued completely positive linear maps on C ∗ -algebras. Then F.H. Szafraniec [14] showed that these theorems are actually equivalent. Due to reasons coming from multivariate stochastic processes R.M. Loynes [7], considered a generalization of B. Sz.-Nagy’s Theorem for vector Hilbert spaces (that he called VH-spaces). These VH-spaces have “inner products” that are vector valued, into the so-called “admissible spaces”. This work is aimed at providing a detailed proof of R.M. Loynes Theorem that generalizes B. Sz.-Nagy, a detailed proof of the equivalence of Stinespring’s Theorem in the Arveson formulation [2] for B∗ -algebras with B. Sz.-Nagy’s Theorem following the lines in [14] together with some ideas from [2], and to get VHvariants of Stinespring’s Theorem for C ∗ -algebras and B∗ -algebras. Relations between these theorems are also considered. | en_US |
| dc.description.degree | M.S. | en_US |
| dc.description.statementofresponsibility | Uğurcan, Barış Evren | en_US |
| dc.format.extent | v, 46 leaves | en_US |
| dc.identifier.uri | http://hdl.handle.net/11693/15359 | |
| dc.language.iso | English | en_US |
| dc.publisher | Bilkent University | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | C-Algebras | en_US |
| dc.subject | VH-Spaces | en_US |
| dc.subject | Completely positive maps | en_US |
| dc.subject | Dilation | en_US |
| dc.subject.lcc | QA326 .U48 2009 | en_US |
| dc.subject.lcsh | C*-algebras. | en_US |
| dc.subject.lcsh | Operator algebras. | en_US |
| dc.subject.lcsh | Dilation theory (Operator theory) | en_US |
| dc.subject.lcsh | Mappings (Mathematics) | en_US |
| dc.title | Dilation theorems for VH-spaces | en_US |
| dc.type | Thesis | en_US |
Files
Original bundle
1 - 1 of 1