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Exercise 3.F.18

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Proof. Suppose $U = 0$ . By 3.106, we have that $\dim U^{0} = \dim V = \dim V^{'}$ . Since $U^{0}$ is a subspace of $V^{'}$ , it follows that $U^{0} = V$ .

Conversely, suppose $U^{0} = V^{'}$ . Using 3.016 again, it follows that $\dim U = 0$ , hence $U = 0$ . □

celiopassos

2017-10-06 00:00

Exercise 3.F.18

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