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55656765

证明:必要性.设${x_n} \in D\left( T \right),\left( {{x_n},T{x_n}} \right) \to \left( {x,y} \right)$,由$T$为闭算子知,$x \in D\left( T \right)$,且$y=Tx$,于是$$\left( {x,y} \right) = \left( {x,Tx} \right) \in G\left( T \right)$$故$G\left( T \right)$为闭集

充分性.设$G\left( T \right)$为闭集,若${x_n} \to x,T{x_n} \to y$,则\[\left( {{x_n},T{x_n}} \right) \to \left( {x,y} \right) \in G\left( T \right)\]这表明$x \in D\left( T \right)$,且$y=Tx$