On the commutativity of sums of Toeplitz operators on the Bergman space
Khitam Aqel, Issam Louhichi
TL;DR
This paper investigates when sums of quasihomogeneous Toeplitz operators commute on the Bergman space, advancing understanding of their algebraic structure and addressing a conjecture related to their bicommutants.
Contribution
It provides new conditions for the commutativity of sums of quasihomogeneous Toeplitz operators, contributing to the theory of operator algebras on the Bergman space.
Findings
Identifies specific conditions under which sums of Toeplitz operators commute.
Progresses towards resolving a conjecture on bicommutants of Toeplitz operators.
Enhances understanding of the algebraic relations among Toeplitz operators.
Abstract
In this paper, we discuss the commutativity of sums of two quasihomogeneous Toeplitz operators on the Bergman space of the unit disc. Our main result goes in the direction of the conjecture in "Bicommutants of Toeplitz operators" (by I. Louhichi and N. V. Rao. Arch. Math. 91, 2008, 256-264)
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Algebraic and Geometric Analysis · Advanced Topics in Algebra