EPSILON-ISOMETRIC EMBEDDINGS

In this paper we study into epsilon-isometries. We prove that if phi is an epsilon-isometry from L(p)(Omega(1), Sigma(1), mu(1)) into L(p)(Omega(2), Sigma(2), mu(2)) (for some p, 1 < p < infinity), then there is a linear operator T : L(p)(Omega(2), Sigma(2), mu(2)) --> L(p)(Omega(1), sigma(1), mu(1)) with parallel to T parallel to = 1 such that parallel to T o phi(f) - f parallel to less than or equal to 6 epsilon for each f epsilon L(p)(Omega(1), Sigma(1), mu(1)). This forms a link between an into isometry result of Figiel and a surjective epsilon-isometry result of Gevirtz in the case of L(p) spaces.