Krein空间中的局部定正规算子
Locally definite normal operators in Krein spaces
摘要：
在Krein空间中引入了双边正型有界正规算子的谱点。证明了正规算子在双侧正型集上存在局部谱函数。此外，我们还证明了仅为正型谱集所对应的Riesz-Dunford谱子空间是一致正的。算子对这个子空间的限制在希尔伯特空间中是正规的。
英文摘要：
We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove that the Riesz-Dunford spectral subspace corresponding to a spectral set which is only of positive type is uniformly positive. The restriction of the operator to this subspace is then normal in a Hilbert space.
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