Algebras Generated by Toeplitz Operators on the Unit Sphere II: Non Commutative Case

Abstract

In Loaiza and Vasilevski (Commutative algebras generated by Toeplitz operators on the unit sphere. Intgr. Equ. Oper. Theory, v. 92, 25 (2020)), we represented the Hardy space H2(S2n−1), with n ≥ 2, as a direct sum of weighted Bergman spaces \(\mathcal {A}^2_p(\mathbb {B}^{n-1})\), with \(p \in \mathbb {Z}_+\), This permitted us to represent Toeplitz operators, whose symbols are invariant under certain \(\mathbb {T}\)-action, acting on H2(S2n−1), as direct sums of Toeplitz operators, acting on corresponding Bergman spaces. As a benefit we were able to use already known results on Toeplitz operators on Bergman spaces, and a wide variety of commutative algebras, generated by Toeplitz operators on H2(S2n−1), was described.