Duality of measures of non-A-compactness

Let A be a Banach operator ideal. Based on the notion of A-compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non-A-compactness of an operator. We consider a map χA (respectively, nA) acting on the operators of the surjective (respectively, injective) hull...

Descripción completa

Detalles Bibliográficos
Autores: Delgado Sánchez, Juan Manuel, Piñeiro Gómez, Cándido
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/96303
Acceso en línea:https://hdl.handle.net/11441/96303
https://doi.org/10.4064/sm7984-1-2016
Access Level:acceso abierto
Palabra clave:Measure of non compactness
Compact set
Operator ideal
p-summing operator
p-compact operator
Essential norm
Descripción
Sumario:Let A be a Banach operator ideal. Based on the notion of A-compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non-A-compactness of an operator. We consider a map χA (respectively, nA) acting on the operators of the surjective (respectively, injective) hull of A such that χA(T) = 0 (respectively, nA(T) = 0) if and only if the operator T is A-compact (respectively, injectively A-compact). Under certain conditions on the ideal A, we prove an equivalence inequality involving χA(T∗) and nAd(T). This inequality provides an extension of a previous result stating that an operator is quasi p-nuclear if and only if its adjoint is p-compact in the sense of Sinha and Karn.