The Mazur–Ulam property for abelian $C^*$-algebras
Volume 266 / 2022
Studia Mathematica 266 (2022), 193-207
MSC: Primary 46B03; Secondary 46B04.
DOI: 10.4064/sm210709-6-12
Published online: 18 May 2022
Abstract
We prove that every abelian $C^*$-algebra $A$ has the Mazur–Ulam property, that is, every surjective isometry $T:S(A)\rightarrow S(E)$ admits an extension to a surjective real linear isometry from $A$ onto $X$.
