Complex Interpolation of Spaces of Operators on l_1

摘要

Within the theory of complex interpolation and θ-Hilbert spaces we extend classical results of Kwapien on absolutely (r, 1)-summing operators on l_1 with values in l_P as well as their natural extensions for mixing operators invented by Maurey. Furthermore, we show that for 1 < P < 2 every operator on l_1 with values in a θ-type 2 space, θ = 2/p', is Rademacher p-summing. This is another extension of Kwapien's results, and by an extrapolation procedure a natural supplement to a statement of Pisier.