The problem of isometric extension in the unit sphere of the space s _p(α)

摘要

In this paper, we present an isometric extension from the unit sphere of a subspace of s_p(α) to the whole space s_p(α). We obtain that the Lamperti isometric mapping of the unit sphere S(s _p(α)) into itself can be extended to an isometry on the whole space s_p(α).