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Schrodinger operators, operators on manifolds, general differential operators, numerical studies, integral operators, discrete models, resonances, non-self-adjoint operators, random operators/matrices

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Orthogonal projection

Let $G$ be an operator with compact resolvent on a Hilbert space $H$ such that $\ker G \neq \{0\}$. Further let $P$ be the orthogonal projection onto $\ker G$, and let $G_{0} := G+P$. My question is: …