Prefer a chat interface with context about you and your work?
A condition equivalent to uniform ergodicity
Let $T$ be a linear operator on a Banach space $X$ with $\mathop {\rm sup}_n \| T^n/n^w\| < \infty $ for some $0\le w < 1$. We show that the following conditions are equivalent: (i) $n^{-1}\sum _{k=0}^{n-1} T^k$ converges uniformly; (ii) ${\rm cl}\, (I -