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Journal of Function Spaces
Volume 2017, Article ID 1730920, 14 pages
https://doi.org/10.1155/2017/1730920
Research Article

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

1Facultad de Matematicas, Universidad Veracruzana, Veracruz, VER, Mexico
2Centro de Investigacion en Matematicas, Guanajuato, GTO, Mexico

Correspondence should be addressed to Raul Quiroga-Barranco; xm.tamic@agoriuq

Received 7 September 2016; Accepted 30 January 2017; Published 3 April 2017

Academic Editor: Hans G. Feichtinger

Copyright © 2017 Miguel Antonio Morales-Ramos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.