Maps Between Fréchet Algebras Which Strongly Preserve Distance One

Abstract

The paper proves that if \( T : X \rightarrow Y \) is a 2-isometry between real linear 2-normed spaces, then \( T \) is affine whenever \( Y \) is strictly convex. It also shows that every surjective mapping \( T : A \rightarrow B \) between real Fréchet algebras, which strongly preserves distance one, is affine under certain conditions.