I have a question: If [itex]x\in X[/itex] is a normed vector space, [itex]X^*[/itex] is the space of bounded linear functionals on [itex]X[/itex], and [itex]f(x) = 0[/itex] for every [itex]f\in X^*[/itex], is it true that [itex]x = 0[/itex]? I'm reasonably confident this has to be the case, but(adsbygoogle = window.adsbygoogle || []).push({}); why? The converse is obviously true, but I don't see why there couldn't be an example of a normed space for which all the functionals in [itex]X^*[/itex] are zero at someothervalue of [itex]x[/itex]...

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# Linear functionals on a normed vector space

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