0
$\begingroup$

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.

$\endgroup$

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

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Community, Mark Viola, BLAZE, Claude Leibovici
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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
3
$\begingroup$

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.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.