Algebraic and Measurable Sub-Product Systems

Abstract

Our main goal, in this thesis, is to conduct a thorough investigation of the math- ematical concept of sub-product system in relation to both quantum dynamical sys- tems and product systems. This notion originates in W. Arveson's pioneering work in non-commutative dynamics theory [5, 7]. The concept has been further extended and analyzed from various perspectives by D. Markiewicz [22], O. Shalit and B. Solel [28], and B.V.R. Bhat and M. Mukherjee [10], among others. The fundamental theme of this thesis is the analysis of relationship between sub- product systems and quantum dynamical semigroups, with emphasis on the role played by certain measurable structures, a role which has often been neglected in the literature. i