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关于复对称算子和C-正规算子的研究

Research on complex symmetric operators and C-normal operators

  • 摘要: 复对称算子与 \boldsymbolC\text- 正规算子的研究在算子理论领域蓬勃发展,已引起众多学者的广泛关注。复对称算子与正规算子和矩阵理论、函数空间算子理论及量子力学等学科存在紧密联系,具有重要的理论与应用价值。本文介绍了复对称算子与 \boldsymbolC\text- 正规算子的基本性质;借助算子分块理论,给出了复对称算子与 \boldsymbolC\text- 正规算子精炼极分解定理的一种新证明;讨论了 \boldsymbolC\text- 正规算子成为复对称算子的充分条件。

     

    Abstract: The study of complex symmetric operators and \boldsymbolC\text- normal operators has flourished in operator theory that has sparked the interest of many scholars. It is closely related to matrix theory, function space operator theory, and quantum mechanics, and has important theoretical and practical significance. In this paper, we introduce the properties of complex symmetric operators and \boldsymbolC\text- normal operators, and give a new method to prove the refined polar decomposition theorem of complex symmetric operators and \boldsymbolC\text- normal operators based on the block operator technique. The sufficient conditions for \boldsymbolC\text- normal operators to complex symmetric operators are also studied.

     

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