Commuting unitary Hilbert space extensions of a pair of Kreĭn space isometries and the Kreĭn-Langer problem in the band (Q1918974)

The authors discuss necessary and sufficient conditions in order that two Krein space isometries with Hilbert defect subspaces admit commuting unitary Hilbert space extensions. The following three cases are analyzed: a) two isometries with regular domains and ranges act in a Krein space; b) only one operator is unitary, while the other has a Hilbert defect subspace; c) both operators are isometries with Hilbert defect subspaces, but one of them is not unitary. The last part of the paper brings contributions to the Krein-Langer problem in the band.