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 Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

2018 ◽  
Vol 13 (2) ◽  
pp. 493-524 ◽  
Author(s):  
Wolfram Bauer ◽  
Raffael Hagger ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Algebras Of Toeplitz Operators ◽  
Dimensional Unit

BOUNDED TOEPLITZ AND HANKEL PRODUCTS ON THE WEIGHTED BERGMAN SPACES OF THE UNIT BALL

2015 ◽  
Vol 99 (2) ◽  
pp. 237-249
Author(s):  
MAŁGORZATA MICHALSKA ◽  
PAWEŁ SOBOLEWSKI
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Hankel Operator ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Necessary Condition ◽  
Sufficient Condition

Let $A_{{\it\alpha}}^{p}$ be the weighted Bergman space of the unit ball in ${\mathcal{C}}^{n}$, $n\geq 2$. Recently, Miao studied products of two Toeplitz operators defined on $A_{{\it\alpha}}^{p}$. He proved a necessary condition and a sufficient condition for boundedness of such products in terms of the Berezin transform. We modify the Berezin transform and improve his sufficient condition for products of Toeplitz operators. We also investigate products of two Hankel operators defined on $A_{{\it\alpha}}^{p}$, and products of the Hankel operator and the Toeplitz operator. In particular, in both cases, we prove sufficient conditions for boundedness of the products.

scholarly journals On the Homology Theory of Operator Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Alaa Hassan Noreldeen
Keyword(s):  
Banach Algebra ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Free Resolution ◽  
Homology Theory ◽  
Cyclic Homology ◽  
Commutative Banach Algebras ◽  
Unital Banach Algebra

We investigate the cyclic homology and free resolution effect of a commutative unital Banach algebra. Using the free resolution operator, we define the relative cyclic homology of commutative Banach algebras. Lemmas and theorems of this investigation are studied and proved. Finally, the relation between cyclic homology and relative cyclic homology of Banach algebra is deduced.

Sign in / Sign up

Export Citation Format

Share Document