Pure E 0 -Semigroups and Absorbing States

Pure E 0 -semigroups and Absorbing States

An E0-semigroup α = {αt : t ≥ 0} acting on B(H) is called pure if its tail von Neumann algebra is trivial in the sense that ∩tαt(B(H)) = C1. We determine all pure E0-semigroups which have a weakly continuous invariant state ω and which are minimal in an appropriate sense. In such cases the dynamics of the state space must stabilize as follows: for every normal state ρ of B(H) there is convergen...

Pure ideals in ternary semigroups

In this paper we introduce the notions of pure ideals, weakly pure ideals in ternary semigroups. We also de ne purely prime ideals of a ternary semigroup and study some properties of these ideals. The space of purely prime two-sided ideal is topologized.

0 Local symmetry properties of pure 3 - qubit states

Entanglement types of pure states of three spin-12 particles are classified by means of their stabilisers in the group of local unitary transformations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.

Convolution Semigroups of States

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C∗-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective cor...

Noncommutative Dynamics and E-semigroups