Geodesic
On holomorphic mappings with relatively p-compact range
Filomat, Tome 37 (2023) no. 24, p. 8067

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DOI

Related to the concept of p-compact operators with p ∈ [1, ∞] introduced by Sinha and Karn [20], 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 ℓ p * or as those whose transposes are quasi p-nuclear operators (respectively, factor through a closed subspace of ℓ p).
DOI : 10.2298/FIL2324067J
Classification : 47B07, 47B10, 46E15, 46E40
Keywords: Vector-valued holomorphic mapping, p-compact set, p-compact operator, locally p-compact holomorphic mapping 
A Jiménez-Vargas. On holomorphic mappings with relatively p-compact range. Filomat, Tome 37 (2023) no. 24, p. 8067 . doi: 10.2298/FIL2324067J
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     author = {A Jim\'enez-Vargas},
     title = {On holomorphic mappings with relatively p-compact range},
     journal = {Filomat},
     pages = {8067 },
     year = {2023},
     volume = {37},
     number = {24},
     doi = {10.2298/FIL2324067J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2324067J/}
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