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.
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