Strictly singular inclusions of rearrangement invariant spaces and Rademacher spaces

• Autorzy: Sergei V. Astashkin , Francisco L. Hernández , Evgeni M. Semenov
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 3
• Strony: 269-283

Daty

wydano

2009

Twórcy

autor

Sergei V. Astashkin

• Department of Mathematics, Samara State University, Samara 443029, Russia

autor

Francisco L. Hernández

• Department of Mathematical Analysis, Madrid Complutense University, 28040 Madrid, Spain

autor

Evgeni M. Semenov

• Department of Mathematics, Voronezh State University, Voronezh 394006, Russia

Identyfikatory

DOI

10.4064/sm193-3-4