Leonard Cadilhac, Sorbonne University
In 2007, M. Junge and Q. Xu made significant contributions to noncommutative ergodic theory and in particular furthered our understanding of non-commutative maximal norms. One of their key results is a Marcinkiewicz-type interpolation theorem for positive maps, for which they provide a rather long and technical proof. I will present a work in collaboration with E. Ricard, where we revisit this theorem, providing a more compact proof and improving on the statement. The talk will first introduce non-commutative maximal norms, then detail the main ideas of proof, and finally discuss extensions of this interpolation result to arbitrary maps.