A Free Approach to p-Compact Type Bounded Holomorphic Mappings

Abstract We introduce and study the classes of free bounded holomorphic mappings between open subsets of complex Banach spaces associated with several types of p -compact sets. Characterizations of such mappings related to linearizations, composition operators and factorizations through a quotient space are stated. We establish some versions for free (weakly) compact holomorphic mappings of the known Schauder Theorem, Gantmacher Theorem and Davis–Figiel–Johnson–Pełczyński Factorization Theorem on linear operators between Banach spaces. The relationships with the classes of p -nuclear and p -integral bounded holomorphic mapping are studied.