Order isomorphisms on function spaces
The classical theorems of Banach and Stone (1932, 1937), Gelfand and Kolmogorov (1939) and Kaplansky (1947) show that a compact Hausdorff space X is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure, respectively, of the space C(X). In this paper, it is shown that for rather general subspaces A(X) and A(Y) of C(X) and C(Y), respectively, any linear bijection T: A(X) → A(Y) such that f ≥ 0 if and only if Tf ≥ 0 gives rise to a homeomorphism...