Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators

2010 ◽  
Vol 66 (1) ◽  
pp. 141-152 ◽  
Author(s):  
Nikolai Vasilevski
Keyword(s):  
Toeplitz Operators ◽  
Banach Algebras ◽  
Algebras Of Toeplitz Operators ◽  
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.

scholarly journals Almost multiplicative functions on commutative Banach algebras

2010 ◽  
Vol 197 (1) ◽  
pp. 93-99 ◽  
Author(s):  
S. H. Kulkarni ◽  
D. Sukumar
Keyword(s):  
Banach Algebras ◽  
Multiplicative Functions ◽  
Commutative Banach Algebras
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