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, Pineiro, 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.
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