Structural properties of universal minimal dynamical systems for discrete semigroups

Structural Properties of Universal Minimal Dynamical Systems for Discrete Semigroups

We show that for a discrete semigroup S there exists a uniquely determined complete Boolean algebra B(S) the algebra of clopen subsets of M(S). M(S) is the phase space of the universal minimal dynamical system for S and it is an extremally disconnected compact Hausdorff space. We deal with this connection of semigroups and complete Boolean algebras focusing on structural properties of these alg...

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

Universal minimal dynamical system for reals

Our aim is to give a description of S(R) and M(R), the phase space of universal ambit and the phase space of universal minimal dynamical system for the group of real numbers with the usual topology.

Structural Properties of Inner Amenable Discrete Groups

Sufficient Conditions for Conservativity of Minimal Quantum Dynamical Semigroups

The conservativity of a minimal quantum dynamical semigroup is proved whenever there exists a " reference " subharmonic operator bounded from below by the dissipative part of the infinitesimal generator. We discuss applications of this criteria in mathematical physics and quantum probability. 1. Introduction A quantum dynamical semigroup (q.d.s.) T = (T t) t≥0 on B(h), the Banach space of bound...