Banach-Stone theorem for quaternion-valued continuous function spaces (Q346964)

Let \(X\) be a compact Hausdorff space. Along the lines of the classical Banach-Stone theorem, the author studies the structure of a surjective real-linear isometry on the space of quaternion-valued continuous functions on \(X\), equipped with the supremum norm. The proof uses the Banach-Stone theorem for isometries of \(\mathbb R^4\)-valued function spaces and the existence of continuous lifts for certain covering maps.