On linear extendability of isometrical embeddings

Abstract

In this paper we first investigate linear extendability of an isometric embedding $T:\mathcal U \longrightarrow \mathcal Y$ from an open subset $\mathcal U$ of a real Banach space $\mathcal X$ into a real Banach space $\mathcal Y$ in the case where $\mathcal Y$ is either the space $C_\Bbb R(K)$ 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 $\mathcal Y$ is an arbitrary real Banach space and $T:\mathcal U \longrightarrow \mathcal Y$ is an isometry whose range satisfies some additional conditions.