Let H = L(0, 1) and let C) be the set of all continuous functions on...

 

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Let H = L(0, 1) and let C) be the set of all continuous functions on [0, 1] that have a continuous derivative. Let te[0, 1] and define L: C1) F by L(h) =h'(t). Show that there is no bounded linear functional on H that agrees with L on C1). Let H = L(0, 1) and let C) be the set of all continuous functions on [0, 1] that have a continuous derivative. Let te[0, 1] and define L: C1) F by L(h) =h'(t). Show that there is no bounded linear functional on H that agrees with L on C1).