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Measures of non-compactness of operators on Banach lattices

Vladimir G. Troitsky
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Abstract

Andreu 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.

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Vladimir G. Troitsky. 2002-10-06. Measures of non-compactness of operators on Banach lattices. https://arxiv.org/abs/math/0210088

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