Let V ;W∞ and W be the operator ideals of completely continuous, weakly ∞-compact, and weakly compact operators, respectively. In a recent paper, William B. Johnson, Eve Oja, and the author proved that V = W∞ ◦W -1 (Johnson, W. B., Lillemets, R., and Oja, E. Representing completely continuous operators through weakly ∞-compact operators. Bull. London Math. Soc., 2016, 48, 452–456). We show that this equality also holds in the context of Banach operator ideals
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