Paired operators and paired kernels
Functional Analysis
2024-01-01 v2
Abstract
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.
Cite
@article{arxiv.2304.07252,
title = {Paired operators and paired kernels},
author = {M. Cristina Câmara and André Guimarães and Jonathan R. Partington},
journal= {arXiv preprint arXiv:2304.07252},
year = {2024}
}
Comments
17 pages. Minor revisions