On the geometry of higher duals of a Banach space
A Banach space \(X\) is said to be an \(M\)-embedded space if the canonical image \(i_X(X)\) is an \(M\)-ideal in the bidual \(X^{**}\) [\textit{P. Harmand, D. Werner} and \textit{W. Werner}, ``\(M\)-ideals in Banach spaces and Banach algebras'', Lect. Notes Math. 1547, Berlin (1993; Zbl 0789.46011)]. It is shown that an \(M\)-embedded, non-reflexive space is an \(M\)-ideal, under the appropriate composition of the canonical embeddings, in all duals of even order. It is deduced that continuous linear functionals on such spaces have unique norm preserving extensions to all even order duals.
scientific article; zbMATH DE number 1734201