Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces
If G is the closure of L∞ in expL2, it is proved that the inclusion between rearrangement invariant spaces E ⊂ F is strictly singular if and only if it is disjointly strictly singular and E 6⊃ G. For any Marcinkiewicz space M(φ) ⊂ G such that M(φ) is not an interpolation space between L∞ and G it is proved that there exists another Marcinkiewicz space M(ψ) ( M(φ) with the property that the M(ψ) and M(φ) norms are equivalent on the Rademacher subspace. Applications are given and a question of Milman answered.