arXiv:2610.35897v1 Announce Type: new Abstract: In this paper, we study the algebraic properties of $\mathcal{S}_\theta$---the class of truncated Toeplitz plus truncated Hankel operators --- on the model space $\mathcal{K}_\theta$. We also give a complete characterization of the intersection class of truncated Toeplitz and truncated Hankel operators under certain conditions. As applications, we describe the non-uniqueness of a decomposition $T=A+B$, show that self-adjoint operators admit self-adjoint decompositions, give a necessary and sufficient inclusion criterion for $\mathcal{S}_\theta$ when $\theta$ is a finite Blaschke product, and, from a first-order commutator characterization of $\mathcal{S}_\theta$, describe the products of its elements and the operators commuting with $S_\theta+ S_\theta^{*}$.
Continue to arXiv Mathematics →You are being forwarded in 6s — stay on this page