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Exercise 6.4.9

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By Theorem 6.15(a) we know that $T (x) = 0$ if and only if $T^{∗} (x) = 0$ . So we get that $N (T) = N (T^{∗})$ . Also, by Exercise 6.3.12 we know that

R (T) = N {(T^{∗})}^{⊥} = N {(T)}^{⊥} = R (T^{∗}) .

jephianlin

2011-06-27 00:00

Exercise 6.4.9

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