How many vectors are needed to compute (p,q)-summing norms?

M. Defant, Marius Junge

We will show that for $q<p$ there exists an $\al < \infty$ such that \[ π_{pq}(T) \pl \le c_{pq} π_{pq}^{[n^α]}(T) \mbox{for all $T$ of rank $n$.}\] Such a polynomial number is onl…