证明：必要性.设${x_n} in Dleft( T ight),left( {{x_n},T{x_n}} ight) o left( {x,y} ight)$，由$T$为闭算子知，$x in Dleft( T ight)$，且$y=Tx$，于是$$left( {x,y} ight) = left( {x,Tx} ight) in Gleft( T ight)$$故$Gleft( T ight)$为闭集
充分性.设$Gleft( T ight)$为闭集，若${x_n} o x,T{x_n} o y$，则[left( {{x_n},T{x_n}} ight) o left( {x,y} ight) in Gleft( T ight)]这表明$x in Dleft( T ight)$，且$y=Tx$