Linear or bilinear mappings between spaces of continuous or Lipschitz functions

摘要

Let K be K or C. The Banach-Stone theorem asserts that, given two locally compact Hausdorff spaces L, M, the surjective linear isometries from C_0(L) to Co(M) are precisely those mapping of the form Tf(t) = p(t)f(σ(t)), where p: M → S_k is continuous and σ: M → L is a homeomorphism. The main consequence of this is that C_0 (M) and C_0(L) are linearly isometric if and only if L and M are hpmeomorphic.