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Using abstract interpolation theory, we study eigenvalue distribution problems for operators on complex symmetric Banach sequence spaces. More precisely, extending two well-known results due to Konig on the asymptotic eigenvalue distribution of operators on l p -spaces, we prove an eigenvalue estimate for Riesz operators on l p -spaces with 1 < p < 2, which take values in a p-concave symmetric Banach sequence space E → l p , as well as a dual version, and show that each operator T on a 2-convex symmetric Banach sequence space F, which takes values in a 2-concave symmetric Banach sequence space E, is a Riesz operator with a sequence of eigenvalues that forms a multiplier from F into E. Examples are presented which among others show that the concavity and convexity assumptions are essential.

Eigenvalue estimates for operators on symmetric Banach sequence spaces