Let (E, ||.||E) be a normed linear space over K and let {ï} be a se- quence in E. Suppose that for every ƒ € E' there exists a positive real number of such that sup{|ƒ(xn)]: n € N} ≤ cf. Prove that there exists a positive real number c such that sup{||n||En €N} ≤ c using the Uniform Boundedness Principle. (Hint: Consider the sequence of functionals {T} in E" defined by Tnf = f(n) for each fc F!

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