On Holomorphic Mappings with Compact Type Range

Abstract

Using Mujica’s linearization theorem, we extend to the holomorphic setting some classical characterizations of compact (weakly compact, Rosenthal, Asplund) linear operators between Banach spaces such as the Schauder, Gantmacher and Gantmacher–Nakamura theorems and the Davis–Figiel–Johnson–Pełczynski, Rosenthal and Asplund factorization theorems.