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Complex interpolation of spaces of operators on l1

Defant A., Michels C.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 3

303-318

Within the theory of complex interpolation and 0-Hilbert spaces we extend classical results of Kwapień 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 on l1 with values in a 0-type 2 space, 0 = 2/p', is Rademacher p-summing. This is another extension of Kwapień's results, and by an extrapolation procedure a natural supplement to a statement of Pisier.