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

TL;DR

This paper provides a counter-example to a theorem about positive operators on Lp spaces with sub-additive power sequences, challenging previous assumptions in functional analysis.

Contribution

It introduces a counter-example that refutes a specific theorem regarding positive operators on Lp spaces with sub-additive power sequences.

Findings

Counter-example disproves the theorem

Challenges previous assumptions in operator theory

Refines understanding of positive operators on Lp spaces

Abstract

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 $L_p\,\,(1<p<\infty)$ which the sequence of the powers is sub-additive.