On linear extendability of isometrical embeddings

In this paper we first investigate linear extendability of an isometric embedding T : u -> y from an open subset u of a real Banach space X into a real Banach space y in the case where y is either the space C-R(K) of continuous real-valued functions on a compact space K, or is a strictly convex Banach space. Then we obtain similar results for the case where Y is an arbitrary real Banach space and T : u -> y is an isometry whose range satisfies some additional conditions.