FA18

Let $T\,$ be a bounded linear operator from a normed space $X\,$ to a normed space $Y\,$ , and its norm be defined by

$||T||=\mathrm{sup}\left\{ ||Tx||:x\isin X, ||x||\le 1\right\}\,$

Show that $||T||=\mathrm{sup}\left\{ ||Tx||:x\isin X, ||x|| = 1\right\}\,$ .