Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, and Cándido Piñeiro. "Duality of measures of non-𝒜-compactness." Studia Mathematica 229.2 (2015): 95-112. <http://eudml.org/doc/285902>.

@article{JuanManuelDelgado2015,
abstract = {Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map $χ_\{\}$ (respectively, $n_\{\}$) acting on the operators of the surjective (respectively, injective) hull of such that $χ_\{\}(T) = 0$ (respectively, $n_\{\}(T) = 0$) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving $χ_\{\}(T*)$ and $n_\{^\{d\}\}(T)$. 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.},
author = {Juan Manuel Delgado, Cándido Piñeiro},
journal = {Studia Mathematica},
keywords = {measure of noncompactness; compact set; operator ideal; -summing operator; -compact operator; essential norm},
language = {eng},
number = {2},
pages = {95-112},
title = {Duality of measures of non-𝒜-compactness},
url = {http://eudml.org/doc/285902},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Juan Manuel Delgado
AU - Cándido Piñeiro
TI - Duality of measures of non-𝒜-compactness
JO - Studia Mathematica
PY - 2015
VL - 229
IS - 2
SP - 95
EP - 112
AB - Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map $χ_{}$ (respectively, $n_{}$) acting on the operators of the surjective (respectively, injective) hull of such that $χ_{}(T) = 0$ (respectively, $n_{}(T) = 0$) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving $χ_{}(T*)$ and $n_{^{d}}(T)$. 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.
LA - eng
KW - measure of noncompactness; compact set; operator ideal; -summing operator; -compact operator; essential norm
UR - http://eudml.org/doc/285902
ER -