Complex interpolation of spaces of operators on l1
Andreas Defant, Carsten Michels
Abstract
Within the theory of complex interpolation and theta-Hilbert spaces we extend classical results of Kwapien on absolutely (r,1)-summing operators on l1 with values in lp as well as their natural extensions for mixing operators invented by Maurey. Furthermore, we show that for 1<p<2 every operator T on l1 with values in theta-type 2 spaces, theta=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.
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