Isometry from l∞ to C[0,1]

Question

Is it possible to define an isometry from l∞ to C[0,1] using disjoint functions?

I can define an isometry from l-p space to L-p space using disjoint functions but I am having difficulties with l∞ to C[0,1].

Answer 1

Such an isometry does not exist, because $C[0,1]$ is separable and $l^\infty$ is not (however, an isometry would preserve this property).