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Functional Analysis

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Let X be a normed space and . Show that if for every bounded linear functional f on X , then .


Solution Preview

let's assume that f : X -> C (the complex numbers) is bounded and linear;
we have the following implications:

f bounded => f is continuous; in particular, f is continuous at 0 (here f(0) = 0 for any f)

in general, the following are equivalent:


Solution Summary

This solution is comprised of a detailed explanation to answer functional analysis.