Let X be a normed space and . Show that if for every bounded linear functional f on X , then .
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:
This solution is comprised of a detailed explanation to answer functional analysis.