Duality of measures of non-𝒜-compactness

Juan Manuel Delgado ; Cándido Piñeiro

Studia Mathematica, Tome 231 (2015), p. 95-112 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2015-01-01

Zbl 1337.47106

EUDML-ID : urn:eudml:doc:285902