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Complex Interpolation of Spaces of Operators on L_1

By Andreas Defant and Carsten Michels


Within the theory of complex interpolation and #-Hilbert spaces we extend classical results of Kwapienonabsolutely(r, 1)-summing operators on # 1 with values in # p as well as their natural extensions f# r mixing operators invented by Maurey Furthermore, we show thatf or 1 <p<2 every operator on # 1 with values in a #-type 2 space, # =2/p # , is Rademacher p-summing.This is another extensionof Kwapien's results, and by an extrapolation procedure a natural supplement to a statement of Pisier. 1991 MSC: 47B10 (primary).46M35 (secondary).Keywords: Complex Interpolation, Absolutely Summing Operators, Grothendieck's Theorem, #-Hilbert spaces.

Year: 2007
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