Sur l'\'enonc\'e d'un th\'eor\`eme concernant les op\'erateurs positifs sur les espaces $L_p$ $(1<p<\mathrm{\infty })$ dont la suite des puissances est sous-additive

In this article we give a counter-example on the statement of a theorem appearing in a note $[3]$ of A. Brunel concerning the study of positive operators on the the spaces $L_p(1<p<\mathrm{\infty })$ which the sequence of the powers is sub-additive.