A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space
Functional Analysis
2025-11-25 v1
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.
Keywords
Cite
@article{arxiv.2511.18041,
title = {A-compact holomorphic Lipschitz mappings on the unit ball of a Banach space},
author = {A. Jiménez-Vargas and D. Ruiz-Casternado},
journal= {arXiv preprint arXiv:2511.18041},
year = {2025}
}
Comments
18 pages