2022/09/08 by A. Jiménez-Vargas, Jiménez-Vargas, A. · 1 citation
Computer Science · Mathematics · #46E15 #46E40 #47B07 #47B10 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2209.03662
openalex publication_date 2022/09/08 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Related to the concept of p-compact operator with p∈ [1,∞] introduced by Sinha and Karn, this paper deals with the space H^∞Kp(U,F) of all Banach-valued holomorphic mappings on an open subset U of a complex Banach space E whose ranges are relatively p-compact subsets of F. We characterize such holomorphic mappings as those whose Mujica's linearisations on the canonical predual of H^∞(U) are p-compact operators. This fact allows us to make a complete study of them. We show that H^∞Kp is a surjective Banach ideal of bounded holomorphic mappings which is generated by composition with the ideal of p-compact operators and contains the Banach ideal of all right p-nuclear holomorphic mappings. We also characterize holomorphic mappings with relatively p-compact ranges as those bounded holomorphic mappings which factorize through a quotient space of ℓp^* or as those whose transposes are quasi p-nuclear operators (respectively, factor through a closed subspace of ℓp).