Definition: Let C[0, 1] denote the real vector space of all continuous real-valued functions on [0, 1]. Define ||f||∞ = sup|f(t)| : t = [0, 1] for ƒ Є C[0, 1]. Let B denote {ƒ Є C[0, 1] : ||ƒ||∞ ≤ 1}. Let P denote the set of all single variable polynomials in C[0, 1]. Problem 4: Find all ƒ € B such that there exist g h Є B with f = .5(g+h). Bonus Problem 5: Find all ƒ Є BNP such that there exist g h Є BNP with f = .5(g+h). Problem 6: Let B₁ = {a € 1¹ : ||a||1 ≤ 1}. Find all a Є B₁ such that such that there exist bcЄ B₁ with a = .5(b+c). Recall from 118A that 1₁ = {a: NR: Σa(n) < ∞,||a||1 = Σ |a(n)|}. n=1 n=1