Mathematic

We will start with a typical example. Let X be a compact Hausdorff space, and let a : X → and ϕ : X → X both be continuous functions. Define T : C(X; ) → C(X; ) by (Tf)(x) = a(x)f(ϕ(x)), if a > 0 on X, then the operator T is linear and positive. For any continuous, positive function f : ...