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arXiv · 2511.18041

A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space

A. Jiménez-Vargas·D. Ruiz-Casternado
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Abstract

Let X and Y be complex Banach spaces, B_X be the open unit ball of X and HL(B_X,Y) be the Banach space of all holomorphic Lipschitz maps f:B_X->Y such that f(0)=0, endowed with the Lipschitz norm. Given a Banach operator ideal A, we use the property of A-compactness by Carl and Stephani to introduce and study the subclass of those functions in HL(B_X,Y) for which its Lipschitz image is a relatively A-compact subset of Y. We focus our attention on its structure as a composition Banach holomorphic Lipschitz ideal by using its connection with A-compact linear operators through linearization/transposition techniques.

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A. Jiménez-Vargas, D. Ruiz-Casternado. 2025-11-22. A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space. https://arxiv.org/abs/2511.18041

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