Dual-band general Toeplitz operators
Functional Analysis
2021-06-04 v2
Abstract
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with matrix symbols. We discuss their norm, their kernel, Fredhomlness, invertibility and spectral properties in various situations, focusing on the spectral properties of the dual-band shift, which turns out to be considerably complex, leading to new and nontrivial connections with the boundary behaviour of the associated inner function.
Cite
@article{arxiv.2012.14725,
title = {Dual-band general Toeplitz operators},
author = {M. Cristina Câmara and Ryan O'Loughlin and Jonathan R. Partington},
journal= {arXiv preprint arXiv:2012.14725},
year = {2021}
}
Comments
30 pages. Title changed from the previous version. Simpler proofs found for some of the later results