doi:10.1002/mana.202300527engAron, RichardDimant, VerónicaGarcía-Lirola, Luis C.Maestre, ManuelLinearization of holomorphic Lipschitz functionsART-2024-138608Let X and Y complex Banach spaces with denoting the open unit ball of . This paper studies various aspects of the holomorphic Lipschitz space , endowed with the Lipschitz norm. This space consists of the functions in the intersection of the sets of Lipschitz mappings and of bounded holomorphic mappings, from to . Thanks to the Dixmier–Ng theorem, is indeed a dual space, whose predual shares linearization properties with both the Lipschitz‐free space and Dineen–Mujica predual of . We explore the similarities and differences between these spaces, and combine techniques to study the properties of the space of holomorphic Lipschitz functions. In particular, we get that contains a 1‐complemented subspace isometric to and that has the (metric) approximation property whenever has it. We also analyze when is a subspace of , and we obtain an analog of Godefroy's characterization of functionals with a unique norm preserving extension in the holomorphic Lipschitz context.2024http://zaguan.unizar.es/record/13532810.1002/mana.202300527http://zaguan.unizar.es/record/135328oai:zaguan.unizar.es:135328info:eu-repo/grantAgreement/ES/DGA/E48-20Rinfo:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C33info:eu-repo/grantAgreement/ES/MICINN/PID2022-137294NB-I00Mathematische Nachrichten 297, 8 (2024), 3024-3051byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess