J-self-adjoint and J-unitary dilations of linear operators (Q1058721)

For a closed linear operator A, defined on a Hilbert space \({\mathfrak H}\), there is constructed a J-selfadjoint operator B on a Hilbert space \({\mathfrak B}\), which contains \({\mathfrak H}\), such that in some neighbourhood of -i we have \(P(B-\lambda I)^{-1}|_{{\mathfrak H}}=(A-\lambda I)^{-1},\) where P is the projection from \({\mathfrak B}\) to \({\mathfrak H}\). A J-unitary dilation of a bounded linear operator on \({\mathfrak H}\) is obtained by similar processes.