Correct selfadjoint and positive extensions of nondensely defined minimal symmetric operators (Q2495039)

A selfadjoint operator \(A\) on a Hilbert space is called correct if it has a bounded inverse \(A^{-1}\). It is known how to describe correct selfadjoint extensions for a positive definite densely defined symmetric operator [\textit{V. I. Gorbachuk} and \textit{M. L. Gorbachuk}, ``Boundary value problems for operator differential equations'' (Kluwer Academic Publishers, Dordrecht etc.) (1991; Zbl 0751.47025)]. The authors consider a nondensely defined symmetric operator \(A_0\) and assume that it has a correct selfadjoint extension \(\hat{A}\). Then they find all correct selfadjoint extensions with the same domain \(D(\hat{A})\) and obtain formulas for their inverses. If \(\hat{A}\) is positive definite, the extensions with the same property are identified among the above set of extensions.