Measures of non-compactness of operators on Banach lattices

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dc.creatorTroitsky, Vladimir G.
dc.date2002-10-06
dc.date.accessioned2026-07-07T04:51:40Z
dc.date.available2026-07-07T04:51:40Z
dc.descriptionAndreu et al [2] and Sadovskii [11] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of de Pagter and Schep [6] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness.
dc.descriptionTo appear in Positivity
dc.identifierhttps://arxiv.org/abs/math/0210088
dc.identifierhttp://arxiv.org/abs/math/0210088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65192
dc.subjectFunctional Analysis
dc.subject47B06, 47B60, 47B65, 47A10, 47B10, 46B08, 46B42, 46B50, 26E35, 46S20
dc.titleMeasures of non-compactness of operators on Banach lattices
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