Throughout this homework Cper ([0, 27], C) denotes the vector space of continuous functions f: (0,21] C such that f(0) = f(27). (This notation is not standard.) 1. Let f e Cper([0, 21), C) and let (fr)n=1 be a sequence of functions in Cper([0, 27), C). (i) Give an example where fn + f in the metric induced by the || . ||2 norm, but fn H f pointwise. (ii) Give an example where fn + f pointwise but fn F f in the metric induced by the || . ||2 norm. Throughout this homework Cper ([0, 27], C) denotes the vector space of continuous functions f: (0,21] C such that f(0) = f(27). (This notation is not standard.) 1. Let f e Cper([0, 21), C) and let (fr)n=1 be a sequence of functions in Cper([0, 27), C). (i) Give an example where fn + f in the metric induced by the || . ||2 norm, but fn H f pointwise. (ii) Give an example where fn + f pointwise but fn F f in the metric induced by the || . ||2 norm