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