If G is the closure of in exp L₂, 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 ⊊ G. For any Marcinkiewicz space M(φ) ⊂ G such that M(φ) is not an interpolation space between 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-4,
author = {Sergei V. Astashkin and Francisco L. Hern\'andez and Evgeni M. Semenov},
title = {Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {269-283},
zbl = {1185.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-4}
}
Sergei V. Astashkin; Francisco L. Hernández; Evgeni M. Semenov. Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces. Studia Mathematica, Tome 192 (2009) pp. 269-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-3-4/