On subinvariant measures for positive operators in L1

We give a counterexample showing that $\bar{(I - T *) L_{\infty}} \cap L_{\infty}^{+} = 0$ 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.

A generalization of the Yosida-Kakutani ergodic theorem

Ezio Marchi, Felipe Zo (1981)

Studia Mathematica

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Coboundaries in $L_{0}^{\infty}$

Dalibor Volný, Benjamin Weiss (2004)

Annales de l'I.H.P. Probabilités et statistiques

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