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• W2890845876 abstract "Let $A_{Q}$ be the self-adjoint operator defined by the $Q$-function $Q:zmapsto Q_{z}$ through the Krein-like resolvent formula $$(-A_{Q}+z)^{-1}= (-A_{0}+z)^{-1}+G_{z}WQ_{z}^{-1}VG_{bar z}^{*},,quad zin Z_{Q},,$$ where $V$ and $W$ are bounded operators and $$Z_{Q}:={zinrho(A_{0}):text{$Q_{z}$ and $Q_{bar z }$ have a bounded inverse}},.$$ We show that $$Z_{Q}not=emptysetquadLongrightarrowquad Z_{Q}=rho(A_{0})cap rho(A_{Q}),.$$ We do not suppose that $Q$ is represented in terms of a uniformly strict, operator-valued Nevanlinna function (equivalently, we do not assume that $Q$ is associated to an ordinary boundary triplet), thus our result extends previously known ones. The proof relies on simple algebraic computations stemming from the first resolvent identity." @default.
• W2890845876 created "2018-09-27" @default.
• W2890845876 creator A5034542231 @default.
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• W2890845876 date "2018-09-13" @default.
• W2890845876 modified "2023-09-27" @default.
• W2890845876 title "On inverses of Krein's Q-functions" @default.
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• W2890845876 hasPublicationYear "2018" @default.
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