Toeplitz operators on the weighted bergman space over the two-dimensional unit ball

We extend the known results on commutative banach algebras generated by toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative banach toeplitz operator algebras. we characterize these new algebras describing their properties and,under a certain extra condition,construct the corresponding gelfand theory. © 2015 alma garcía and nikolai vasilevski.