Wu jingbo.Normal Extensions of Operators to Krein Spaces[J].Chinese Annals of Mathematics B,1987,8(1):36~42
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Authors：
Wu jingbo;
Abstract：
In this paper, it is proved that every bounded linear operator on a Hilbert space has a normal extension to a Krein space. Two criteria for J-subnormality are given. In particular, in order that T be subnormal, it suffices that exp(-\bar \Lambda T^*)exp(\Lambda T) be a positive definite operator function on a bounded infinite subset of complex plane. This improves the condition of Bram [4]. Also it is proved that the local spectral subspaces are closed for J-subnormal operators.
