This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter 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.
- Pub Date:
- February 2010
- Mathematics - Operator Algebras;
- Mathematical Physics;
- Mathematics - Functional Analysis;
- Quantum Physics;
- PhD. thesis (Technion, Haifa). 195 pages. Supervisor: Baruch Solel. Defended on June 2009