Kernels of paired operators and their adjoints

2024/08/26 by M. Cristina Câmara, Jonathan R. Partington, Câmara, M. Cristina +1
Mathematics · #30H10 #47B35 #47B38 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2408.14120

openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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