Give an example of a linear mapping from a normed space into a normed space which is not continuous.

Question

Give an example of a linear mapping from a normed space into a normed space which is not continuous.

I can't think of anything. Any help would be very appreciated.

Answer 1

Hint: try checking that $P([0,1]) \ni p \mapsto p' \in P([0,1])$ is not bounded in the unit sphere. Here $P([0, 1])$ is the space of polynomials in $[0,1]$, with the sup norm.