On Lindenstrauss-Pełczyński spaces

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

Abstrakty

EN

We consider some stability aspects of the classical problem of extension of C(K)-valued operators. We introduce the class ℒ𝒫 of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c₀ into them can be extended to c₀. We show that all ℒ𝒫-spaces are of type $ℒ_{∞}$ but not conversely. Moreover, $ℒ_{∞}$-spaces will be characterized as those spaces E such that E-valued operators from w*(l₁,c₀)-closed subspaces of l₁ extend to l₁. Regarding examples we will show that every separable $ℒ_{∞}$-space is a quotient of two ℒ𝒫-spaces; also, $ℒ_{∞}$-spaces not containing c₀ are ℒ𝒫-spaces; the complemented subspaces of C(K) and the separably injective spaces are subclasses of the ℒ𝒫-spaces and we show that the former does not contain the latter. Regarding stability properties, we prove that quotients of an ℒ𝒫-space by a separably injective space and twisted sums of ℒ𝒫-spaces are ℒ𝒫-spaces.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 3
• Strony: 213-231

Daty

wydano

2006

Twórcy

autor

Jesús M. F. Castillo

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

autor

Yolanda Moreno

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

autor

Jesús Suárez

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

Identyfikatory

DOI

10.4064/sm174-3-1