Three-space problems and bounded approximation properties

• Autorzy: Wolfgang Lusky
• Języki publikacji: EN

Abstrakty

EN

Let ${Rₙ}_{n=1}^{∞}$ be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an $ℒ_{p}$-space, then both X and A have bases. We apply these results to show that the spaces $C_{Λ} = \overline{span}{z^{k} : k ∈ Λ} ⊂ C(𝕋)$ and $L_{Λ} = \overline{span}{z^{k} : k ∈ Λ} ⊂ L₁(𝕋)$ have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 159
• Numer: 3
• Strony: 417-434

Daty

wydano

2003

Twórcy

autor

Wolfgang Lusky

• Institute for Mathematics, University of Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany

Identyfikatory

DOI

10.4064/sm159-3-6