Abstract The application of the general tensor norms theory of Defant and Floret to the ideal of ( p , σ )‐absolutely continuous operators of Matter, 0 < σ < 1, 1 ≤ p < ∞ leads to the study of g p ′, σ ‐nuclear and g p ′, σ ‐integral operators. Characterizations of such operators has been obtained previously in the case p > 1. In this paper we characterize the g ∞, σ ‐nuclear and g ∞, σ ‐integral operators by the existence of factorizations of some special kinds. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)