Radial Toeplitz operators on bounded symmetric domains 11:10 Fri 9 Mar, 2018 :: Lower Napier LG11 :: Raul Quiroga-Barranco :: CIMAT, Guanajuato, Mexico
The Bergman spaces on a complex domain are defined as the space of holomorphic square-integrable functions on the domain. These carry interesting structures both for analysis and representation theory in the case of bounded symmetric domains. On the other hand, these spaces have some bounded operators obtained as the composition of a multiplier operator and a projection. These operators are highly noncommuting between each other. However, there exist large commutative C*-algebras generated by some of these Toeplitz operators very much related to Lie groups. I will construct an example of such C*-algebras and provide a fairly explicit simultaneous diagonalization of the generating Toeplitz operators.