Multilinear isometries on function algebras

Abstract

Let be function algebras (or more generally, dense subspaces of uniformly closed function algebras) on locally compact Hausdorff spaces , respectively, and let Z be a locally compact Hausdorff space. A -linear map is called a multilinear (or k-linear) isometry ifBased on a new version of the additive Bishop’s Lemma, we provide a weighted composition characterization of such maps. These results generalize the well-known Holsztyński’s theorem and the bilinear version of this theorem provided in Moreno and Rodríguez [Studia Math. 2005;166:83–91] by a different approach.