2-SUMMING OPERATORS ON I2(X)

Let X = (X-n)(n is an element of N) be a sequence of Banach spaces and I-2 (X), c(0) (X) the corresponding vector valued sequence spaces. In this paper we characterize nuclear operators on c(0) (X). As an application we obtain the necessary condition for an operator on I-2 (X) to be 2-summing. In the case of multiplication operators from I-2 (X) into I-2(Y) (respectively from c(0) (X) into c(0) (Y) we show that the sufficient condition stated by Nahoum is also necessary. We also give the necessary and sufficient conditions for a bounded linear operator from I-2(H) into I-2(H) to he 2-summing, where H and K are sequences of Hilbert spaces. Further we give the necessary and/or sufficient conditions that Hardy and Hilbert type operators from I-2 (X) into I-2(Y) to be 2-summing.