Abstract Let X and Y be complex Banach spaces, BX B X be the open unit ball of X and HL₀ (BX, Y) H L 0 (B X, Y) be the Banach space of all holomorphic Lipschitz maps f: BX Y f: B X → Y such that f (0) =0 f (0) = 0, endowed with the Lipschitz norm. Given a Banach operator ideal A A, we use the property of A A -compactness by Carl and Stephani to introduce and study the subclass of those functions in HL₀ (BX, Y) H L 0 (B X, Y) for which its Lipschitz image is a relatively A A -compact subset of Y. We focus our attention on its structure as a composition Banach holomorphic Lipschitz ideal by using its connection with A A -compact linear operators through linearization/transposition techniques.
Jiménez-Vargas et al. (Thu,) studied this question.