2021/10/21 by María Cueto-Avellaneda, Daisuke Hirota, Cueto-Avellaneda, María +5 · 1 citation
Mathematics · #17C65 #46B04 #46B20 #46J10 #46J15 #47B49 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2110.11120
openalex publication_date 2021/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 goal we study surjective isometries between the unit spheres of two abelian JB^*-triples represented as spaces of continuous functions of the form C^\mathbbT0 (X) := \ a ∈ C0(X) : a (λt) = λa(t) \hbox for every (λ, t) ∈ \mathbbT× X\, where X is a (locally compact Hausdorff) principal \mathbbT-bundle. We establish that every surjective isometry Δ: S(C0^\mathbbT(X))→ S(C0^\mathbbT(Y)) admits an extension to a surjective real linear isometry between these two abelian JB^*-triples.