Singular perturbations with an infinite constant coupling (Q1966308)

The author is developing the theory of selfadjoint operators \(A\) in the Hilbert space \(H\) with perturbation \(\alpha V\) when \(\alpha\) is a parameter tending to infinity, \(V\) is an operator having dense zeros in \(H\). It is supposed that the operators \(A\) and \(\lim_{\alpha\to\infty} (A+\alpha V)= A_\infty\) are mutually simple, see [\textit{N. I. Akhiezer} and \textit{I. M. Glazman}, ``Theory of linear operators in Hilbert space'', Boston (1981; Zbl 0467.47001)]. It is proved that the operator \(A+\alpha V\) is selfadjoint in \(H\) and the convergence \(A+\alpha V\) takes place on \(\alpha\to \infty\) to the limit \(A_\infty\) in the strong resolvent sense.