operator valued series and vector valued multiplier spaces

‎let x,y be normed spaces with l(x,y) the space of continuous‎ ‎linear operators from x into y‎. ‎if tj is a sequence in l(x,y),‎ ‎the (bounded) multiplier space for the series sumtj 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 s:minfty(sumtj)rightarrowy associated‎ ‎with the series is defined to be s(xj)=suminftyj=1tjxj.‎ ‎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.‎