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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:
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