Abstract
[Indag. Math.(N.S.) 2(2) (1991), 149–158; Uspehi Mat. Nauk 27(1(163)) (1972), 81–146] 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 [J. Funct. Anal. 78(1) (1988), 31–55] 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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Troitsky, V.G. Measures of Non-compactness of Operators on Banach Lattices. Positivity 8, 165–178 (2004). https://doi.org/10.1023/B:POST.0000042833.31340.6b
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DOI: https://doi.org/10.1023/B:POST.0000042833.31340.6b