Abstract
Applying a linearization theorem due to Mujica (Trans Am Math Soc 324:867–887, 1991), we study the ideals of bounded holomorphic mappings mathcal {I}circ mathcal {H}^infty generated by composition with an operator ideal mathcal {I}. The bounded-holomorphic dual ideal of mathcal {I} is introduced and its elements are characterized as those that admit a factorization through mathcal {I}^{textrm{dual}}. For complex Banach spaces E and F, we also analyze new ideals of bounded holomorphic mappings from an open subset Usubseteq E to F such as p-integral holomorphic mappings and p-nuclear holomorphic mappings with 1le p<infty . We prove that every p-integral (p-nuclear) holomorphic mapping from U to F has relatively weakly compact (compact) range.
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