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For linear operators, if 1 ≤ p ≤ q < ∞, then every absolutely p-summing operator is also absolutely q-summing. On the other hand, it is well known that for n ≥ 2, there are no general "inclusion theorems" for absolutely summing n-linear mappings or n-homogeneous polynomials. In this paper we deal with situations in which the spaces of absolutely p-summing and absolutely q-summing linear operators coincide, and prove that for 1 ≤ p ≤ q ≤ 2 and n ≥ 2, we have inclusion theorems for absolutelydoi:10.1090/s0002-9939-08-09394-5 fatcat:yq2dccxpdreu5ol6blowglmglm