On Certain Subshifts and their Associated Monoids

Within a subclass of monoids (with zero) a structural characterization is given of those that are associated to topologically transitive subshifts with Property (A).Comment: 11 page

Type III0\text{III}_0 cocycles without unbounded gaps

summary:An example of type III$_0$ cocycle without unbounded gaps of an ergodic probability measure preserving transformation will be shown

Type III0\text{III}_0 cocycles without unbounded gaps

summary:An example of type III$_0$ cocycle without unbounded gaps of an ergodic probability measure preserving transformation will be shown

On measure theoretical analogues of the Takesaki structure theorem for type III factors

The orbit equivalence of type $III_{0}$ ergodic equivalence relations is considered. We show that it is equivalent to the outer conjugacy problem for the natural trace-scaling action of a countable dense ℝ-subgroup by automorphisms of the Radon-Nikodym skew product extensions of these relations. A similar result holds for the weak equivalence of arbitrary type $III_{0}$ cocycles with values in Abelian groups