Abstract
We study the weighted Banach spaces of vector-valued holomorphic functions defined on an open and connected subset of a Banach space. We use linearization results on these spaces to get conditions which ensure that a functionfdefined in a subsetAof an open and connected subsetUof a Banach spaceX, with values in another Banach spaceE, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.
Highlights
The property of being norming for subspaces in E∗ is between weak∗-dense and strongly dense
The injection of l1(M) in E is an onto isomorphism
If we assume in Lemma 2 that M is 1-norming, the isomorphism is an isometry
Summary
The property of being norming for subspaces in E∗ is between weak∗-dense and strongly dense. Let AV(U) be a subspace of HV(U) which has a τc-compact closed unit ball, let A ⊆ U be a set of uniqueness for AV(U), and let E be a Banach space.
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