Toeplitz operators, pseudo-homogeneous symbols and moment maps on the complex projective space

TL;DR

This paper introduces a new class of symbols for Toeplitz operators on complex projective space, establishing their commutativity and geometric interpretation via moment maps, and extends these results to the unit ball.

Contribution

It defines quasi-radial pseudo-homogeneous symbols on projective space and introduces extended pseudo-homogeneous symbols, expanding the class of commutative Toeplitz operator algebras.

Findings

Establishment of commutativity for Toeplitz operators with these symbols.

Geometric interpretation of symbols through moment maps.

Construction of larger commutative Banach algebras.

Abstract

Following previous works for the unit ball, 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.