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Normal extensions of operators to Krein spaces. (English) Zbl 0641.47043

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

MSC:

47B50 Linear operators on spaces with an indefinite metric
47A20 Dilations, extensions, compressions of linear operators
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