Holomorphic mappings on l₁

We describe the holomorphic mappings of bounded type, and the arbitrary holomorphic mappings from the complex Banach space l₁ into a complex Banach space X. It is shown that these mappings have monomial expansions and the growth of the norms of the coefficients is characterized in each case. This characterization is used to give new descriptions of the compact open topology and the Nachbin ported topology on the space H(li; X) of holomorphic mappings, and to prove a lifting property for holomorphic mappings on l\. We also show that the monomials form an equicontinuous unconditional Schauder basis for the space H(l₁), T₀) of holomorphic functions on 11 with the topology of uniform convergence on compact sets.