Product systems, subproduct systems and dilation theory of completely positive semigroups

Details Product systems, subproduct systems and dilation theory of completely positive semigroups Product systems, subproduct systems and dilation theory of completely positive semigroups

2010-02-26

arxiv.org/abs/1002.4920v1

Mathematics

Operator Algebras

PhD. thesis (Technion, Haifa). 195 pages. Supervisor: Baruch Solel. Defended on June 2009

Scientific paper

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.

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