Linearization of holomorphic Lipschitz functions

Aron, Richard ; Dimant, Verónica ; García-Lirola, Luis C. (Universidad de Zaragoza) ; Maestre, Manuel

Resumen: Let 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.

Idioma: Inglés

DOI: 10.1002/mana.202300527

Año: 2024

Publicado en: Mathematische Nachrichten 297, 8 (2024), 3024-3051
ISSN: 0025-584X

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C32
Financiación: info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/PID2021-122126NB-C33
Financiación: info:eu-repo/grantAgreement/ES/MCINN/PID2022-137294NB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)