RT journal article
T1 The Bishop-Phelps-Bollobás Property for Weighted Holomorphic Mappings
A1 Jiménez-Vargas, A.
A1 Ramírez, M.I.
A1 Villegas Vallecillos, Moisés
A2 Matemáticas
K1 46B20
K1 46E50
K1 46T25
K1 Bishop–Phelps–Bollobás property
K1 norm attaining operator
K1 Weighted holomorphic function
AB Given an open subset U of a complex Banach space E, a weight v on U and a complex Banach space F, let Hv∞(U,F) denote the Banach space of all weighted holomorphic mappings from U into F, endowed with the weighted supremum norm. We introduce and study a version of the Bishop–Phelps–Bollobás property for Hv∞(U,F) (WH∞-BPB property, for short). A result of Lindenstrauss type with sufficient conditions for Hv∞(U,F) to have the WH∞-BPB property for every space F is stated. This is the case of Hvp∞(D,F) with p≥1, where vp is the standard polynomial weight on D. The study of the relations of the WH∞-BPB property for the complex and vector-valued cases is also addressed as well as the extension of the cited property for mappings f∈Hv∞(U,F) such that vf has a relatively compact range in F.
PB Birkhauser
SN 1420-9012
YR 2024
FD 2024
LK http://hdl.handle.net/10498/33669
UL http://hdl.handle.net/10498/33669
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026