Algebras Generated by Toeplitz Operators on the Hardy Space over the Siegel Domain

Abstract

Following the approach of Loaiza and Vasilevski (Equ Oper Theory 92(3): 33, 2020, https://doi.org/10.1007/s00020-020-02580-x ; “Operator Theory, Functional Analysis and Applications”, Oper Theory Adv Appl 28(2), 2020, to appear), we give two different representations of the Hardy space on the Siegel domain in terms of the Bergman space and terms of the direct integral of the weighted Fock spaces. Based on these representations we describe then various commutative and non-commutative $$C^*$$ -algebras, which are generated by Toeplitz operators acting on the Hardy space over the Siegel domain.