PDEA Seminar: The Spectra of Toeplitz Operators and Sums of Ray Operators

Abstract: Ray operators are a certain type of semi-infinite linear operator. Sums of constant ray operators are unitarily equivalent to a multiplication operator followed by projection. This is analogous to the well-known Toeplitz operators, which are also unitarily equivalent to multiplication-then-projection operators. The spectra of Toeplitz operators can be nicely approximated by finite dimensional Toeplitz matrices via a concept known as the pseudospectrum. This leads to questioning whether the pseudospectrum is a useful technique in investigating the spectrum of radially constant operators. Additionally, I will discuss an application of ray operators to the number theoretic Bose-Hubbard dimer model.

This is a seminar in the PDEs and Applications seminar series.