设P是X中相对应于闭线性子空间Y的投影算子.对任意x belongs to X,exsit x1 belongs to Y,x2 belongs to Y(垂直符号)， which x=x1+x2,Px=x1, for x1,x1=x1+0, where x1 belongs to Y,0 belongs to Y(垂直符号)，so Px1=x1,P^2 x=Px1=Px, that means P^2=P