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Suppose you're looking at a complex vector space X, and you know that, for some x in X, you have f(x) = 0 for every linear map on X. Can you conclude that x = 0? If so, how?

This seems easy, but I can't think of it for some reason.

(EDIT: Assume it holds for every CONTINUOUS (i.e., bounded) linear map on X. This may, or may not, make a difference.)

This seems easy, but I can't think of it for some reason.

(EDIT: Assume it holds for every CONTINUOUS (i.e., bounded) linear map on X. This may, or may not, make a difference.)

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