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

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