Question: Let V denote a linear functional on, ie, range V-(-x, x) and Viaf by) a()+ big) for all f. ge2, It is continuous whenever 1-1,

Let V denote a linear functional on, ie, range V-(-x, x) and Viaf by) a()+ big) for all

f. ge2, It is continuous whenever 1-1, 0, and V is hounded if is C,1, for all fe where C, is a finite constant. Prove that a continuous linear functional is bounded Hint: Otherwise, there existe,with 1.1, o(1) but (>1 whence ifg,

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