We prove the result stated in the title; that is, every separable Banach space is linearly isometric to a closed subspace E of the space of continuous functions on [ 0, 1 ], such that every nonzero ...

Let A be a finite-dimensional commutative algebra over R and let Cr A (U), Cω (U, A) and OA (U) be the ring of A-differentiable functions of class Cr, 0 ≤ r ≤ ∞, the ring of real analytic mappings ...