Artículo
On null sequences for Banach operator ideals, trace duality and approximation properties
Fecha de publicación:
10/2017
Editorial:
Wiley VCH Verlag
Revista:
Mathematische Nachrichten
ISSN:
0025-584X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (ℓ1;X),c0,A(X) behaves much alike c0(X). When this is the case we give a geometric tensor product representation of c0,A(X). On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of c0,A(X). We apply our results to study some problems related with the KA -approximation property giving a trace condition which is used to solve the remaining case (p=1) of a problem posed by Kim (2015). Namely, we prove that if a dual space has the K1 -approximation property then the space has the Ku,1 -approximation property.
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; On null sequences for Banach operator ideals, trace duality and approximation properties; Wiley VCH Verlag; Mathematische Nachrichten; 290; 14-15; 10-2017; 2308-2321
Compartir
Altmétricas