Mathematics Department, New Mexico State University Las Cruces, NM 88003,USA
Abstract
Let be normed spaces with the space of continuous linear operators from into . If is a sequence in , the (bounded) multiplier space for the series is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator associated with the series is defined to be . In the scalar case the summing operator has been used to characterize completeness, weakly unconditionall Cauchy series, subseries and absolutely convergent series. In this paper some of these results are generalized to the case of operator valued series The corresponding space of weak multipliers is also considered.
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