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.


closed as off-topic by user99914, Mark Viola, user147263, BLAZE, Claude Leibovici Nov 13 '15 at 5:54

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  • $\begingroup$ You can search for "not continuous linear operator" in this site and you will surely find one, but don't give up, try to find one on your own! $\endgroup$ – dafinguzman Nov 13 '15 at 3:39
  • $\begingroup$ Possible duplicate of Discontinuous linear functional $\endgroup$ – user147263 Nov 13 '15 at 4:24

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.


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