Banach spaces of continuous vector-valued functions of ordinals (Q2716976)

Let \(X\) be a Banach space and \(\xi\) an ordinal number. The Banach space of the continuous \(X\)-valued functions defined in the interval of ordinals \([1, \xi]\) equipped with the supremum norm is denoted by \(X^{\xi}\).NEWLINENEWLINENEWLINEHere, by using the continuum hypothesis, the author gives an isomorphic classification of \(C(I)^{\xi}\) for \(\xi \geq \omega_1\). Moreover a characterization of the separable Banach space \(X\) that are isomorphic to \(X^{\xi}\) for \(\omega \leq \xi \leq \omega_1\) is given.