Exercise 1.4: A linear continuous functional with predescribed values (4 points) Consider a normed space X over K € {R,

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Exercise 1 4 A Linear Continuous Functional With Predescribed Values 4 Points Consider A Normed Space X Over K R 1 (28.67 KiB) Viewed 40 times

Exercise 1.4: A linear continuous functional with predescribed values (4 points) Consider a normed space X over K € {R, C}, a sequence (j)jeN in X, a sequence (α;)jen in K and let y € (0,0). Prove that there exists a' X' such that 'x ≤y and x'(x) = ax; for all j € N if and only if the inequality 72 n sy [₁,₂ holds for all n N and arbitrary choices of a sequence (3₁)jen in K. jEN