$\cdot$ Let $T: C[-1,1] \rightarrow \mathbb{R}, T(f)=\int_{-1}^{1} e^{t} f(t) d t$ (a) Show that $N(T)$ is a complete subspace of $C[-1,1]$. (b) Show that the set $\{f \in C[-1,1]: f$ is odd $\} \varsubsetneqq N(T)$. CS.VS.1583|

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