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首页> 外文期刊>Journal of the Mathematical Society of Japan >Domination of unbounded operators and commutativity
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Domination of unbounded operators and commutativity

机译：控制无界算子和可交换性

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摘要

It is proved that pointwise commuting formally normal operators which are dominated by a single essentially normal operator are essentially normal and essentially spectrally commuting. The question when essential normality of a polynomial in an operator implies essential normality of that operator is solved in this way. Furthermore, domination by essentially normal powers of formally normal operators are studied and, as a consequence, extended versions of Nelson's criterion for essential spectral commutativity are proposed. Subsequent domination results ensuring joint subnormality of systems of operators are proved. Several applications to multidimensional moment problems are found.
机译：已经证明，由单个基本法线算符支配的逐点形式上的正规法线算符是基本法线和本质上是频谱交换的。以这种方式解决了在运算符中多项式的基本正态性暗示该运算符的基本正态性的问题。此外，还研究了形式上正规算子的基本正规幂的支配力，因此，提出了用于基本频谱可交换性的纳尔逊准则的扩展版本。证明了随后的支配结果，可确保运营商系统的联合次正规性。发现了多维矩量问题的几种应用。

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