Finite rank transformation and weak closure theorem
Finite rank transformation and weak closure theorem
We introduce a new class of cocycles which provides examples of measure preserving dynamical systems (X,B,μ,T), such that given positive integers r⩾2 and m⩾1, possibly infinite, with (r,m)≠(∞,∞), the rank is r and the order of the quotient group in the measure-theoretic centralizer, #C(T)wcl{Tn;n∈Z}, is m. Moreover, wcl{Tn;n∈Z} is uncountable. …