The structure of Lindenstrauss-Pełczyński spaces

• Autorzy: Jesús M. F. Castillo , Yolanda Moreno , Jesús Suárez
• Języki publikacji: EN

Abstrakty

EN

Lindenstrauss-Pełczyński (for short ℒ𝒫) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ𝒫-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative answer to a problem posed by Lindenstrauss and Pełczyński [J. Funct. Anal. 8 (1971)]. We show that the class of ℒ𝒫-spaces does not have the 3-space property, which corrects a theorem in an earlier paper of the authors [Studia Math. 174 (2006)]. We then solve a problem in that paper showing that $ℒ_{∞}$ spaces not containing l₁ are not necessarily ℒ𝒫-spaces.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 2
• Strony: 105-115

Daty

wydano

2009

Twórcy

autor

Jesús M. F. Castillo

• Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, España

autor

Yolanda Moreno

• Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, España

autor

Jesús Suárez

• Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, España

Identyfikatory

DOI

10.4064/sm194-2-1