Completely p-summing maps on the operator Hilbert space OH

We prove the completely p-summing ideals of OH are all equal as sets for 1⩽p<2. A phase transition then occurs at p=2 as we also show for p⩾2, the completely p-summing ideals of OH turn out as sets to be Schatten ideal classes with the limiting case being the Schatten 4-class ideal S4 when p→∞.