Toeplitz operators on the domain (Formula Presented)- with (Formula Presented)-invariant symbols
Let D be the irreducible bounded symmetric domain of 2 × 2 complex matrices that satisfy ZZ* < I2. The biholomorphism group of D is realized by U(2, 2) with isotropy at the origin given by U(2) ×U(2). Denote by (Formula Presented) the subgroup of diagonal matrices in U(2). We prove that the set of (Formula Presented)-invariant essentially bounded symbols yield Toeplitz operators that generate commutative C*-algebras on all weighted Bergman spaces over D. Using tools from representation theory, we also provide an integral formula for the spectra of these Toeplitz operators.
Publication Source (Journal or Book title)
Operator Theory: Advances and Applications
Dawson, M., Ólafsson, G., & Quiroga-Barranco, R. (2020). Toeplitz operators on the domain (Formula Presented)- with (Formula Presented)-invariant symbols. Operator Theory: Advances and Applications, 279, 79-101. https://doi.org/10.1007/978-3-030-44651-2_9