Toeplitz Operators, Pseudo-Homogeneous Symbols, and Moment Maps on the Complex Projective Space

Abstract

Following previous works for the unit ball due to Nikolai Vasilevski, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in terms of moment maps is developed. This leads us to the introduction of a new family of symbols, extended pseudo-homogeneous, that provide larger commutative Banach algebras generated by Toeplitz operators. This family of symbols provides new commutative Banach algebras generated by Toeplitz operators on the unit ball.