Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper is devoted to the study of weakly continuous holomorphic functions on pseudoconvex domains in Banach spaces with Schauder bases. We establish the identity of pseudoconvex domains and domains of existence of weakly continuous holomorphic functions. We show that holomorphic functions can be approximated by weakly continuous holomorphic functions. We study the spectra of certain algebras of weakly continuous holomorphic functions.232435452Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [06/02378-7, 04/07441-7]