Quantum Stochastic Cocycles and Completely Bounded Semigroups on Operator Spaces II

Quantum stochastic cocycles provide a basic model for time-homogeneous Markovian evolutions in quantum setting, and direct counterpart continuous time to random walks, both the Schrodinger Heisenberg pictures. This paper is sequel one which correspondences were established between classes of cocycle on an operator space or C*-algebra, Schur-action `global' semigroup associated matrix spaces over space. In this we investigate generation via their corresponding global semigroups, with primary purpose strengthening scope applicability theory analysis construction cocycles. An explicit description given affine relationship generator completely bounded any its semigroups. Using this, structure positive quasicontractive C*-algebra whose expectation norm derived, giving comprehensive generalisation Christensen--Evans extension GKS&L theorem Gorini, Kossakowski Sudarshan, Lindblad. The transformation also provides new existence unbounded map as generator. latter applied interacting particles known exclusion Markov process, particular integer lattices dimensions two.