On property (β) of Rolewicz in Köthe-Bochner sequence spaces

• Autorzy: Henryk Hudzik , Paweł Kolwicz
• Języki publikacji: EN

Abstrakty

EN

We study property (β) in Köthe-Bochner sequence spaces E(X), where E is any Köthe sequence space and X is an arbitrary Banach space. The question of whether or not this geometric property lifts from X and E to E(X) is examined. We prove that if dim X = ∞, then E(X) has property (β) if and only if X has property (β) and E is orthogonally uniformly convex. It is also showed that if dim X < ∞, then E(X) has property (β) if and only if E has property (β). Our results essentially extend and improve those from [14] and [15].

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 3
• Strony: 195-212

Daty

wydano

2004

Twórcy

autor

Henryk Hudzik

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Paweł Kolwicz

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland

Identyfikatory

DOI

10.4064/sm162-3-1