Let $ X $ be a Hilbert space, $ A_n, A $ be symmetric closed operators on $ X $ which satisfies \begin{equation*} {s.g.-\lim}_{n \to \infty} A_n = A \quad (\textrm{Strong graph convergence}) \end{equation*} For $ x_n \in \mathcal{N}(A_n) $, if $ x_n \stackrel{w}{\longrightarrow} x $, can we determine that $ x \in \mathcal{D}(A) $?
2026-04-12 01:17:52.1775956672
Weak convergence for symmetric closed operators?
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