Kernels of Paired Operators and Their Adjoints

M. Cristina Câmara () and Jonathan R. Partington ()
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M. Cristina Câmara: Universidade de Lisboa, Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico
Jonathan R. Partington: University of Leeds, School of Mathematics

Chapter 76 in Operator Theory, 2026, pp 2365-2388 from Springer

Abstract: 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.

Keywords: Paired operator; Transposed paired operator; Toeplitz operator; Invariant subspace; Almost-invariant subspace; Nearly-invariant subspace; Truncated Toeplitz operator; Kernel (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16356-1_107

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