Local dual spaces of a Banach space

• Autorzy: Manuel González , Antonio Martínez-Abejón
• Języki publikacji: EN

Abstrakty

EN

We study the local dual spaces of a Banach space X, which can be described as the subspaces of X* that have the properties that the principle of local reflexivity attributes to X as a subspace of X**.
We give several characterizations of local dual spaces, which allow us to show many examples. Moreover, every separable space X has a separable local dual Z, and we can choose Z with the metric approximation property if X has it. We also show that a separable space containing no copies of ℓ₁ admits a smallest local dual.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B10: Duality and reflexivity
• 46B04: Isometric theory of Banach spaces
• 46B08: Ultraproduct techniques in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 147
• Numer: 2
• Strony: 155-168

Daty

wydano

2001

Twórcy

autor

Manuel González

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain

autor

Antonio Martínez-Abejón

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo, Spain

Identyfikatory

DOI

10.4064/sm147-2-4