Normal extensions of operators to Krein spaces (Q1100715)

A bounded linear operator T on a Hilbert space H is called J-subnormal of order n if there exists a bounded J-normal operator \(\tilde T\) on a Pontrjagin space \(\Pi_ n\) containing H, such that \(\tilde T|_ H=T\) and the vectors \(T^{*k}f\), \(f\in H\), generate \(\Pi_ n\). The former theorem establishes the existence of a normal extension to a Krein space. Then there are proved two criteria of J-subnormality, which improve some previous results. The J-subnormal operators have remarkable properties as for example the single-valued extension property, the non- dominance of their adjoints, etc.