Wu, Jingbo Normal extensions of operators to Krein spaces. (English) Zbl 0641.47043 Chin. Ann. Math., Ser. B 8, 36-42 (1987). 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. Reviewer: T.Balan Cited in 4 Documents MSC: 47B50 Linear operators on spaces with an indefinite metric 47A20 Dilations, extensions, compressions of linear operators Keywords:J-normal operator; Pontrjagin space; existence of a normal extension to a Krein space; J-subnormal operators; single-valued extension property; non-dominance of their adjoints PDFBibTeX XMLCite \textit{J. Wu}, Chin. Ann. Math., Ser. B 8, 36--42 (1987; Zbl 0641.47043)