The Banach-Saks property in rearrangement invariant spaces

• Autorzy: P. G. Dodds , E. M. Semenov , F. A. Sukochev
• Języki publikacji: EN

Abstrakty

EN

This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the Banach-Saks property.

Kategorie tematyczne

• 46A30: Open mapping and closed graph theorems; completeness (including B -, B r -completeness)
• 46B20: Geometry and structure of normed linear spaces
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 3
• Strony: 263-294

Daty

wydano

2004

Twórcy

autor

P. G. Dodds

• School of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, Australia

autor

E. M. Semenov

• Department of Mathematics, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394693, Russia

autor

F. A. Sukochev

• School of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, Australia

Identyfikatory

DOI

10.4064/sm162-3-6