Canonical forms of unbounded unitary operators in Krein spaces
Let \({\mathcal K}_ i\) \((i=1,2)\) be Krein spaces such that dim(\({\mathcal K}^+_ 1)=\dim ({\mathcal K}^+_ 2)\) and dim(\({\mathcal K}^-_ 1)=\dim ({\mathcal K}^-_ 2)\). The author presents a canonical form of a (not necessarily bounded) Krein-space unitary operator from \({\mathcal K}_ 1\) to \({\mathcal K}_ 2\), which maps \({\mathcal K}^+_ 1\) to a maximal positive subspace \({\mathcal L}\) of \({\mathcal K}_ 2\), in terms of the angular operator of \({\mathcal L}\) and Hilbert-space unitary operators \(V_+\) (resp. \(V_-)\) from \({\mathcal K}^+_ 1\) to \({\mathcal K}^+_ 2\) (resp. from \({\mathcal K}^- _ 1\) to \({\mathcal K}^-_ 2)\).
scientific article; zbMATH DE number 4086377