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One of the statements, Corollary 3.7, in [1] is erroneous. In fact, the hypothesis that W is a separating subspace of X has to be replaced by the stronger hypothesis that W is almost norming. The arguments are implicitely in [1]. We give precise statements and proofs. Let X be a Banach space and W a separating subspace of the dual space X of X, i.e., for all x ∈ X \ {0} there exists ϕ ∈ W such that ϕ(x) = 0. Then we may identify X with a subspace of W , the dual space of W . To say that W is almost norming means by definition thatis an equivalent norm on X. This is equivalent to saying that X is closed in W . By a result of Davis and Lindenstrauss [1, Remark 1.2] each separating subspace of X is almost norming if and only if dim X /X < ∞. Now we first formulate and prove the corrected version of [1, Corollary 3.7]. Theorem 1. Let ⊂ C be open and connected. Let A ⊂ have a limit point in and let h : A → X be a function. Assume that there exist c ≥ 0, an almost norming subspace W of X and a family {H ϕ : ϕ ∈ W } of holomorphic functions on such that H ϕ (z) = ϕ, h(z) (ϕ ∈ W, z ∈ A)and |H ϕ (z)| ≤ c ϕ (ϕ ∈ W, z ∈ ) .Then h has a holomorphic extension to with values in X.

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