Let $A_0:\mathcal{H} \supset \mathcal{D}(A_0) \to \mathcal{H}$ be a densely defined (by $\mathcal{D}(A_0)$ I denote a domain of an operator $A_0$), closed and self-adjoint operator acting on a separable Hilbert space $\mathcal{H}$ and let $z \in \rho(A_0)$, so there exist $(A_0 - zI)^{-1}$ and it is bounded. Let $V: \mathcal{H} \supset \mathcal{D}(V) \to \mathcal{H}$ be a densely defined symmetric operator and $\mathcal{D}(A_0)\subset \mathcal{D}(V)$. My question is, if it is true that $z \in \rho(A_0+V)$?
2026-03-27 07:00:07.1774594807
Resolvent set of perturbed operator
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