Vector-valued holomorphic functions revisited

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A weak criterion for vector-valued holomorphy (2004, methodology): “In contrast to the approach chosen in [2] we do not rely on the equivalence of holomorphy and weak holomorphy due to Dunford and Grothendieck, where a function f : Ω → E is called weakly holomorphic if x′ ◦ f : Ω → C is holomorphic for all x′ ∈ E′.”