FA18

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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\in X,||x||\leq 1\right\}\,

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