Abstract In this paper, we develop the injective and interpolative procedures to generate holomorphic Lipschitz ideals A^ {HL₀}. Based on the injective procedure of Pietsch for operator ideals, the concept of injective hull of A^ {HL₀}, denoted by (A^ {HL₀}) ^inj, is introduced and characterized in terms of a domination property. A description of the closed injective hull of A^ {HL₀} is established in terms of an Ehrling-type inequality. Building upon the interpolative procedure of Matter for operator ideals, we also present the concept of interpolative hull of A^ {HL₀}, denoted by (A^ {HL₀}) for [0, 1). We prove that (A^ {HL₀}) is an injective holomorphic Lipschitz ideal which is located between the injective hull and the closed injective hull of A^ {HL₀}. We describe the (closed) injective hull of holomorphic Lipschitz ideals generated by composition and duality with Banach operator ideals A, and these descriptions are applied to concrete examples of holomorphic Lipschitz ideals.
Dahia et al. (Mon,) studied this question.
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