Product systems, subproduct systems and dilation theory of completely positive semigroups
Abstract
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats twoparameter semigroups, and contains also contributions to dilation theory of product system representations. The second part deals with completely positive semigroups parameterized by quite general semigroups, where the major technical tool introduced is subproduct systems and their representations. In the third part subproduct systems are studied, together with the multivariable operator theory and operator algebras they give rise to.
 Publication:

arXiv eprints
 Pub Date:
 February 2010
 arXiv:
 arXiv:1002.4920
 Bibcode:
 2010arXiv1002.4920S
 Keywords:

 Mathematics  Operator Algebras;
 Mathematical Physics;
 Mathematics  Functional Analysis;
 Quantum Physics;
 46L55;
 46L57;
 46L08;
 47L30;
 47D03;
 47H20
 EPrint:
 PhD. thesis (Technion, Haifa). 195 pages. Supervisor: Baruch Solel. Defended on June 2009