On Composition Ideals and Dual Ideals of Bounded Holomorphic Mappings

Abstract

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