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→∞. © 2008 Elsevier Inc. All rights reserved.