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Spectral inequalities for compact integral operators on Banach function spaces. (English) Zbl 0795.47020
Summary: This article generalizes some spectral inequalities for non-negative matrices to compact integral operators with non-negative kernels defined on Banach function spaces. The spectral radius of a sum of such operators is estimated under certain conditions and a generalization of this inequality is given. An inequality for the spectral radius of a compact integral operator with the kernel equal to a weighted geometric mean of non-negative kernels is also proved.

MSC:
47B38 Linear operators on function spaces (general)
47A10 Spectrum, resolvent
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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References:
[1] Zaanen, Riesz Spaces 2 (1983)
[2] Luxemburg, Banach Function Spaces (1955)
[3] DOI: 10.1007/BF02760610 · Zbl 0438.47042 · doi:10.1007/BF02760610
[4] DOI: 10.1080/03081088808817892 · Zbl 0684.15007 · doi:10.1080/03081088808817892
[5] DOI: 10.1016/0024-3795(89)90380-7 · Zbl 0687.15013 · doi:10.1016/0024-3795(89)90380-7
[6] Kerin, Functional Analysis and Measure Theory pp 199– (1962)
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