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Exercise 2.6.15

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If $T^{t} (f) = fT = 0$ , this means $f (y) = 0$ for all $y \in R (T)$ and hence $f \in {(R (T))}^{0}$ . If $f \in {(R (T))}^{0}$ , this means $f (y) = 0$ for all $y \in R (T)$ and hence $T^{t} (f) (x) = f (T (x)) = 0$ for all $x$ . This means $f$ is an element in $N (T^{t})$ .

jephianlin

2011-06-27 00:00

Exercise 2.6.15

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