Different extensions of linear operators on euclidean space

Question

In the euclidean space $\mathbb{R}^n$, it's possible to find a linear subspace $Y \subseteq \mathbb{R}^n$ and a linear and bounded operator $l \in Y'$ such that $l$ has two different extensions $T_1, T_2$ in the dual of $\mathbb{R}^n$ such that $ \left\|{T_1}\right\|= \left\|{T_2}\right\|= \left\|{l}\right\|$? I think that it's possible if $Y$ is not dense in $\mathbb{R}^n$, but I could not find some example.