prove that a non constant linear functional from a normed linear space X is discontinuous if and only if Z(f) = {x in X | f(x) = 0} is dense in X.

Asked Feb 13 '16 at 12:32

Active Feb 13 '16 at 12:32

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I could prove that if Z(f) is dense in X then the functional must me discontinuous but I am not able to prove the other way round

asked Feb 13 '16 at 12:32

numeric_atom

this question is asked many times on the site. – Svetoslav Feb 13 '16 at 12:36
can you send me the link with an answer? – numeric_atom Feb 13 '16 at 12:43
http://math.stackexchange.com/questions/123282/linear-functional-on-a-banach-space-is-discontinuous-then-its-nullspace-is-dense – Svetoslav Feb 13 '16 at 12:46
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http://math.stackexchange.com/questions/1432705/f-is-discontinuous-iff-kernelf-is-dense-in-x for both directions – Svetoslav Feb 13 '16 at 12:48

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