On holomorphic mappings with compact type range

TL;DR

This paper extends classical linear operator characterizations to the holomorphic setting using Mujica's linearization theorem, broadening the understanding of compactness and related properties in complex analysis.

Contribution

It introduces a novel approach to holomorphic mappings by applying linearization techniques to generalize key operator theorems from Banach space theory.

Findings

Extended Schauder, Gantmacher, and Gantmacher-Nakamura theorems to holomorphic mappings

Generalized Davis-Figiel-Johnson-Pelczynski, Rosenthal, and Asplund factorization theorems for holomorphic contexts

Established new characterizations of compact and weakly compact holomorphic mappings

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-Pelczynski, Rosenthal and Asplund factorization theorems.