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arXiv · 2209.02956

On composition ideals and dual ideals of bounded holomorphic mappings

M. G. Cabrera-Padilla·A. Jiménez-Vargas·D. Ruiz-Casternado
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Abstract

Applying a linearization theorem due to J. Mujica, we study the ideals of bounded holomorphic mappings $\mathcal{H}^\infty\circ\mathcal{I}$ 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 $\mathcal{I}^\mathrm{dual}$. For complex Banach spaces $E$ and $F$, we also analyze new ideals of bounded holomorphic mappings from an open subset $U\subseteq E$ to $F$ such as $p$-integral holomorphic mappings and $p$-nuclear holomorphic mappings with $1\leq p<\infty$. We prove that every $p$-integral ($p$-nuclear) holomorphic mapping from $U$ to $F$ has relatively weakly compact (compact) range.

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M. G. Cabrera-Padilla, A. Jiménez-Vargas, D. Ruiz-Casternado. 2022-09-07. On composition ideals and dual ideals of bounded holomorphic mappings. https://arxiv.org/abs/2209.02956

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