Measures of non-compactness of operators on Banach lattices
Functional Analysis
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0210088,
title = {Measures of non-compactness of operators on Banach lattices},
author = {Vladimir G. Troitsky},
journal= {arXiv preprint arXiv:math/0210088},
year = {2007}
}
Comments
To appear in Positivity