Geodesic
On invariant measures for power bounded positive operators
Studia Mathematica, Tome 120 (1996) no. 2, pp. 183-189

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-120-2-183-189
Keywords: power bounded and Cesàro bounded positive operators, invariant measures, $L_1$ spaces

Ryotaro Sato 1

1 
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Ryotaro Sato. On invariant measures for power bounded positive operators. Studia Mathematica, Tome 120 (1996) no. 2, pp. 183-189. doi: 10.4064/sm-120-2-183-189

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