scholarly journals On the structure of commutative Banach algebras generated by Toeplitz operators on the unit ball. Quasi-elliptic case. I: Generating subalgebras

2013 ◽  
Vol 265 (11) ◽  
pp. 2956-2990 ◽  
Author(s):  
Wolfram Bauer ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Banach Algebras ◽  
Elliptic Case ◽  
Commutative Banach Algebras

scholarly journals Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Alma García ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Weighted Bergman Space ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Extra Condition ◽  
Dimensional Unit ◽  
Commutative Banach Algebras

We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Miguel Antonio Morales-Ramos ◽  
Raul Quiroga-Barranco ◽  
Armando Sanchez-Nungaray
Keyword(s):  
Projective Space ◽  
Unit Ball ◽  
Complex Projective Space ◽  
Toeplitz Operators ◽  
Banach Algebras ◽  
Geometric Interpretation ◽  
Moment Maps ◽  
New Family ◽  
Commutative Banach Algebras ◽  
Complex Projective

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.

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