Majorization, Interpolation and noncommutative Khintchine inequalities

Léonard Cadilhac

Published 2018-12-10Version 1

We give a new characterization of interpolated spaces for the couple $(L_p(0,\alpha),L_q(0,\alpha))$, $0<p<q<\infty$ in terms of two forms of majorization. The result is closely related to the characterization obtained by computing the $K$-functional. This extends the work of Cwikel and Nilsson which treated the case of Banach sequence spaces. We apply it to study characterizations of spaces in which noncommutative Khintchine inequalities hold.