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Following previous works for the unit ball, we define quasi-radialpseudo-homogeneous symbols on the projective space and obtain the correspondingcommutativity results for Toeplitz operators. A geometric interpretation ofthese symbols in terms of moment maps is developed. This leads us to theintroduction of a new family of symbols, extended pseudo-homogeneous, thatprovide larger commutative Banach algebras generated by Toeplitz operators.This family of symbols provides new commutative Banach algebras generated byToeplitz operators on the unit ball.

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