On null sequences for Banach operator ideals, trace duality and approximation properties

Authors
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro
Publication Year
2017
Language
English
Format
article
Status
Published version
Description
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.
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Subject
46B45; SECONDARY: 46B28
46B50
APPROXIMATION PROPERTIES
COMPACT SETS
NULL SEQUENCES
OPERATOR IDEALS
PRIMARY: 46B04
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Restricted access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/55551