Abstract
In this note we present two new positive answers to Tingley’s problem in certain subspaces of function algebras. In the first result we prove that every surjective isometry between the unit spheres, S(A) and S(B), of two uniformly closed function algebras A and B on locally compact Hausdorff spaces can be extended to a surjective real linear isometry from A onto B. In a second part we study surjective isometries between the unit spheres of two abelian JB*-triples represented as spaces of continuous functions of the form
where X is a (locally compact Hausdorff) principal -bundle and
denotes the unit sphere of ℂ. We establish that every surjective isometry
admits an extension to a surjective real linear isometry between these two abelian JB*-triples.