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.
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