An approximation property with respect to an operator ideal

• Autorzy: Juan Manuel Delgado , Cándido Piñeiro
• Języki publikacji: EN

Abstrakty

EN

Given an operator ideal 𝒜, we say that a Banach space X has the approximation property with respect to 𝒜 if T belongs to $\overline{S∘T: S ∈ ℱ(X)}^{τ_{c}}$ for every Banach space Y and every T ∈ 𝒜(Y,X), $τ_{c}$ being the topology of uniform convergence on compact sets. We present several characterizations of this type of approximation property. It is shown that some of the existing approximation properties in the literature may be included in this setting.

Kategorie tematyczne

• 47L20: Operator ideals
• 46B50: Compactness in Banach (or normed) spaces
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 1
• Strony: 67-75

Daty

wydano

2013

Twórcy

autor

Juan Manuel Delgado

• Departamento de Matemática Aplicada I, Escuela Técnica Superior de Arquitectura, Avenida Reina Mercedes, 2, 41012 Sevilla, Spain

autor

Cándido Piñeiro

• Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario del Carmen, 21071 Huelva, Spain

Identyfikatory

DOI

10.4064/sm214-1-4