Answer to Question #7454 in Functional Analysis for Vince

Question #7454

Let E be a dense linear subspace of a normed vector space X, and let Y be a
Banach space. Suppose T_0 in £(E, Y) is a bounded linear operator from E to Y.
Show that To can be extended to T in £(X, Y) (by continuity) without increasing
its norm.

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