Prove that -- the range $R(T)$ of a bounded linear operator $T:X\to Y$ need not be closed in $Y$

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Prove that the range $R(T)$ of a bounded linear operator $T:X\to Y$ need not be closed in $Y$.

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Consider the identity map $$\mbox{id} :\ell^1 \longrightarrow \ell^2 .$$