Necessity of approximate Kakutani structure for irreducible weighted shifts
Let TTT be an irreducible weighted shift with weights {αn}n=1∞\{\alpha_n\}_{n=1}^{\infty}{αn}n=1∞. For each n∈Nn\in\mathbb{N}n∈N and ϵ>0\epsilon>0ϵ>0, suppose there is an index cn,ϵ≥nc_{n,\epsilon}\geq ncn,ϵ≥n su…