Example to linear but not continuous

Question

We know that when $(X,\|\cdot\|_X)$ is finite dimensional normed space and $(Y,\|\cdot\|_Y)$ is arbitrary dimensional normed space if $T:X \to Y$ is linear then it is continuous (or bounded)

But I cannot imagine example for when $(X,\|\cdot\|_X)$ and $(Y,\|\cdot\|_Y)$ are arbitrary dimensional normed spaces $T:X \to Y$ is linear and not bounded or continuous.

Could someone give any simple example please?

Thanks

Answer 1

The differentiation operator is noncontinuous (not bounded) on the space $\Bbb R[x]$ of all polynomials with $\sup$ norm over $[-1,1]$.