p-Compact holomorphic mappings

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)) is an element of l(p)(E), K subset of {Sigma(n) a(n)x (n) | (a(n)) is an element of B(lp)(1)}. In [4], Delgado, Oja, Pieiro, 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.