Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1

• Autorzy: F. Albiac , C. Leránoz
• Języki publikacji: EN

Abstrakty

EN

We prove that the quasi-Banach spaces $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$ (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $ℓ₁(c₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

Kategorie tematyczne

• 46A40: Ordered topological linear spaces, vector lattices
• 46A35: Summability and bases
• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 46A45: Sequence spaces (including K\"othe sequence spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 150
• Numer: 1
• Strony: 35-52

Daty

wydano

2002

Twórcy

autor

F. Albiac

• Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain

autor

C. Leránoz

• Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain

Identyfikatory

DOI

10.4064/sm150-1-4