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We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and also, somewhat surprisingly, their stark differences. Various notions expressing different invariance properties are also reviewed, and we extend to paired operators some known invariance results.

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Kernels of Paired Operators and Their Adjoints

  • 动态工具书词条

  • 发表日期：

    2025年

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  • M. Cristina Câmara,
  • Jonathan R. Partington

摘要

We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and also, somewhat surprisingly, their stark differences. Various notions expressing different invariance properties are also reviewed, and we extend to paired operators some known invariance results.