Let B(X) be the space of bounded functionals on a metric space X (example 2.11). Let T:

Question:

Let B(X) be the space of bounded functionals on a metric space X (example 2.11). Let T: B(X) → B(X) be an increasing function with property that for every constant c ∊ ℜ
T(f + c) = T(f) + βc for every f ∊ B(X) (21)
for some 0 ≤ ft < 1. Show that T is a contraction with modulus β.