P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II

Abstract

AbstractLet be a semifinite von Neumann algebra equipped with an increasing filtration of (semifinite) von Neumann subalgebras of . For , let denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration and the index . We prove the following real interpolation identity: If and , then This is new even for classical martingale Hardy spaces as it is previously known only under the assumption that the filtration is regular. We also obtain an analogous result for noncommutative column martingale Orlicz–Hardy spaces.