On invariant measures for power bounded positive operators
Volume 120 / 1996
Studia Mathematica 120 (1996), 183-189
DOI: 10.4064/sm-120-2-183-189
Abstract
We give a counterexample showing that $\overline{(I-T*)L_{∞}} ∩ L^{+}_{∞} = {0}$ does not imply the existence of a strictly positive function u in $L_1$ with Tu = u, where T is a power bounded positive linear operator on $L_1$ of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.
