Computing p-summing norms with few vectors

Abstract

It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only ``few&#34; vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, ``few&#34; means n if 1<p<2 and n^{p/2} if 2<p<infinity.