On injective and interpolative procedures for holomorphic Lipschitz ideals

In this paper, we develop the injective and interpolative procedures to generate holomorphic Lipschitz ideals AHL₀ . Based on the injective procedure of Pietsch for operator ideals, the concept of injective hull of AHL₀ , denoted by (AHL₀)ⁱⁿʲ , is introduced and characterized in terms of a domination property. A description of the closed injective hull of AHL₀ 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 AHL₀ , denoted by (AHL₀)σ for σ ∈ [0,1) . We prove that (AHL₀)σ is an injective holomorphic Lipschitz ideal which is located between the injective hull and the closed injective hull of AHL₀ . 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.