Vector lattice structure in spaces of absolutely summing operators (Q1113070)

Let X, Y be Banach spaces and T be a bounded operator from X to Y. The operator T is p-absolutely summing \((p>0)\), if \[ (1)\quad (\sum^{n}_{k=1}\| Tx_ k\|^ p)^{1/p}\leq C \sup \{(\sum^{n}_{k=1}| <x',x_ k>|^ p)^{1/p}\}, \] where \(x'\in X^*\), \(\| x'\| \leq 1\). The space \(\Pi_ p(X,Y)\) of p- absolutely summing operators is investigated.