Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

Sergei V. Astashkin, Francisco L. Hernández, and Evgeni M. Semenov. "Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces." Studia Mathematica 193.3 (2009): 269-283. <http://eudml.org/doc/285103>.

@article{SergeiV2009,
abstract = {If G is the closure of $L_\{∞\}$ 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 $L_\{∞\}$ 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.},
author = {Sergei V. Astashkin, Francisco L. Hernández, Evgeni M. Semenov},
journal = {Studia Mathematica},
keywords = {rearrangement invariant spaces; strict singularity; Rademacher subspace},
language = {eng},
number = {3},
pages = {269-283},
title = {Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces},
url = {http://eudml.org/doc/285103},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Sergei V. Astashkin
AU - Francisco L. Hernández
AU - Evgeni M. Semenov
TI - Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 3
SP - 269
EP - 283
AB - If G is the closure of $L_{∞}$ 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 $L_{∞}$ 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.
LA - eng
KW - rearrangement invariant spaces; strict singularity; Rademacher subspace
UR - http://eudml.org/doc/285103
ER -