Abstract
Following Sinha and Karn [9], a relatively compact subset K of a Banach space E is said to be p-compact if for some sequence (x n ) ∈ l p (E), K ⊂ {Σ n a x x n | (a n ) ∈ B ℓ′ p }. In [4], Delgado, Oja, Piñeiro, and Serrano investigated the p-approximation property, in which one only requires finite rank approximation of the identity on p-compact subsets. We investigate analogous concepts here for the case of holomorphic mappings between Banach spaces, introducing the space of p-compact holomorphic mappings (cf. [1]). A number of problems related to such holomorphic mappings are discussed.
Resumen.
Según Sinha y Karn [9], un subconjunto relativamente compacto K de un espacio de Banach E es p-compacto si para alguna sucesión (x n ) ∈ l p (E), K ⊂ {Σ n a x x n | (a n ) ∈ B ℓ′ p }. En [4], Delgado, Oja, Piñeiro, y Serrano investigaron la propiedad de p-aproximación, en la que sólo se requiere aproximaciones en conjuntos p-compactos. En este trabajo investigamos conceptos análogos para aplicaciones holomorfas entre espacios de Banach, introduciendo el espacio de aplicaciones holomorfas p-compactas (cf. [1]). También presentamos una colección de problemas relacionados con dichas aplicaciones.
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In honor of Don Manuel Valdivia, who has always searched for and, almost always, solved problems
Submitted by J. Bonet
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Aron, R.M., Maestre, M. & Rueda, P. p-Compact holomorphic mappings. RACSAM 104, 353–364 (2010). https://doi.org/10.5052/RACSAM.2010.22
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DOI: https://doi.org/10.5052/RACSAM.2010.22