Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces
Volume 193 / 2009
Studia Mathematica 193 (2009), 269-283
MSC: Primary 46E30.
DOI: 10.4064/sm193-3-4
Abstract
If is the closure of L_\infty in \exp L_{2}, it is proved that the inclusion between rearrangement invariant spaces E\subset F is strictly singular if and only if it is disjointly strictly singular and E\not\supset G. For any Marcinkiewicz space M(\varphi) \subset G such that M(\varphi) is not an interpolation space between L_{\infty} and G it is proved that there exists another Marcinkiewicz space M(\psi)\subsetneq M(\varphi) with the property that the M(\psi) and M(\varphi) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.
