On \(C^\ast\)-algebras of Toeplitz operators on the harmonic Bergman space
Algebras of Toeplitz operators acting on the harmonic Bergman space \(b^2({\mathbb D})\) of the unit disk are studied. \(C^*\)-algebras generated by Toeplitz operators are described in the following three different cases: (1) Toeplitz operators with bounded radial symbols in the elliptic case; (2) Toeplitz operators with piecewise continuous symbols in the parabolic case; (3) Toeplitz operators with piecewise continuous symbols in the hyperbolic case. It is shown that the corresponding Calkin algebras are commutative in the first two cases and not commutative in the last case.
scientific article; zbMATH DE number 6175201
scientific article