I want to show, Image of $unit~ disc$ under a discontinuous linear functional from a Normed Linear Space is $\mathbb{C}$ . I know the Image is Unbounded

  • $\begingroup$ What it is $unit dis$? Is it the unit sphere or the unit ball? $\endgroup$ – shuhalo Mar 18 '11 at 9:59
  • $\begingroup$ ${x\in X : ||x|| \le 1}$ $\endgroup$ – SION Mar 18 '11 at 10:04

Hint: a discontinuous linear functional is still linear! So if $f(x)=z$, consider $f(wx)$, where $|w|=1$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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