Duality of measures of non-𝒜-compactness

• Autorzy: Juan Manuel Delgado , Cándido Piñeiro
• Języki publikacji: EN

Abstrakty

EN

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 $χ_{𝒜}$ (respectively, $n_{𝒜}$) acting on the operators of the surjective (respectively, injective) hull of 𝒜 such that $χ_{𝒜}(T) = 0$ (respectively, $n_{𝒜}(T) = 0$) 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 $χ_{𝒜}(T*)$ and $n_{𝒜^{d}}(T)$. 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.

Kategorie tematyczne

• 47H08: Measures of noncompactness and condensing mappings, K -set contractions, etc.
• 47L20: Operator ideals
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 229
• Numer: 2
• Strony: 95-112

Daty

wydano

2015

Twórcy

autor

Juan Manuel Delgado

• Departamento de Matemática Aplicada I, Escuela Técnica Superior de Arquitectura Avenida Reina Mercedes, 2, 41012 Seville, Spain

autor

Cándido Piñeiro

• Departamento de Matemáticas, Facultad de Ciencias Experimentales, Campus Universitario de El Carmen, 21071 Huelva, Spain

Identyfikatory

DOI

10.4064/sm7984-1-2016