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Exercise 5.B.6

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Proof. It is easy to see that $T^{k} u \in U$ for $u \in U$ and non-negative $k$ (this can easily be proven by induction on $k$ ). Since $p (T) u$ is a sum of terms like this, multiplied by the coefficients of $p$ , and $U$ is closed under addition and scalar multiplication, then $p (T) u \in U$ . □

celiopassos

2017-10-06 00:00

Exercise 5.B.6

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