2023/04/14 by M. Cristina Câmara, Câmara, M. Cristina, André Luiz Sena Guimarães +3
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Advanced Harmonic Analysis Research
paper · pdf · doi:10.48550/arxiv.2304.07252
This paper is concerned with paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space. By considering when such operators commute, generalizations of the Brown--Halmos results for Toeplitz operators are derived. Further, the kernels of such operators are described, giving results on invariant and nearly-invariant subspaces, together with a generalization of Coburn's theorem on Toeplitz kernels.