Spectral inequalities for compact integral operators on Banach function spaces

This article generalizes some spectral inequalities for non-negative matrices (see [2] and [3]) 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.