F-quotients and envelope of F-holomorphy

Abstract

Let E be a complex Banach space, let F be a closed subspace of E, and let π: E → E F be the canonical quotient mapping. The concept of envelope of F-holomorphy of a connected open subset U of E is defined and studied. The main result states that the pull-back E ∗(U) of the envelope of holomorphy of π( U) constructed by Schottenloher is the envelope of F-holomorphy of U.