Изменения
Нет описания правки
$\varphi \in \operatorname{Ker}A^*$, $A^* \varphi = 0$, $\forall x \in E: A^*(\varphi, x) = 0, A^*(\varphi, x) = \varphi(A x) \implies \varphi(A x) = 0$
$y \in R(A) \implies y = Ax, \varphi \in \operatorname{Ker} A^* \implies \varphi y = \varphi(A x) = 0 \implies R(A) \subset (\operatorname{Ker}A^*)^\perp$
$y \in \operatorname{Cl} R(A), y = \lim y_n, y_n \in R(A), \varphi \in \operatorname {Ker}^* (A)$ $\varphi(y_n) = 0, \varphi(y_n) \xrightarrow[]{n \to \infty} \varphi(y) \implies \operatorname{Cl}(R(A)) \subset (\operatorname{Ker}(A^*))^\perp$ $\implies y \in (\operatorname{Ker}A^*)^\perp \implies(?) y \in \operatorname{Cl}(R(A))$
