Vol. 63, No. 2, 1976

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Analytic extensions of vector-valued functions

Josip Globevnik

Vol. 63 (1976), No. 2, 389–395

Let Δ be the open unit disc in C, Δ its boundary and B Δ a relatively open set. Let X be a complex Banach space. Denote by HB,X) the set of all continuous functions from Δ B to X which are analytic on Δ. A set P X is said to have the analytic extension property with respect to HB,X) if for each relatively closed set F B of Lebesgue measure 0 and for each continuous function f : F P there exists g HB,X) with gF = f and gB) P.

Theorem. Let P X be an open set. Then P has the analytic extension property with respect to HB,X) for every relatively open B Δ if and only if P is connected.

Mathematical Subject Classification 2000
Primary: 46E15
Secondary: 30A96
Received: 30 September 1975
Published: 1 April 1976
Josip Globevnik