2023/11/23 by A. Jiménez-Vargas, Jiménez-Vargas, A., M. I. Ramírez +3 · 1 citation
Mathematics · #46B20 #46E50 #46T25 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2311.14070
openalex publication_date 2023/11/23 · openalex created_date 2023/11/28 · openalex updated_date 2026/07/28
Given an open subset U of a complex Banach space E, a weight v on U and a complex Banach space F, let H^∞v(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 H^∞v(U,F) (WH^∞-BPB property, for short). A result of Lindenstrauss type with sufficient conditions for H^∞v(U,F) to have the WH^∞-BPB property for every space F is stated. This is the case of H^∞vp(\mathbbD,F) with p≥ 1, where vp is the standard polynomial weight on \mathbbD. 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∈ H^∞v(U,F) such that vf has relatively compact range in F.