Commutative C*-algebras of Toeplitz operators on the unit ball, II.: Geometry of the level sets of symbols

被引：34

作者：

Quiroga-Barranco, Raul ^{[1
]}

Vasilevski, Nikolai ^{[2
]}

机构：

[1] Ctr Invest Matemat, Guanajuato 36000, Gto, Mexico

[2] CINVESTAV, Dept Matemat, Mexico City 07000, DF, Mexico

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2008年 / 60卷 / 01期

关键词：

Toeplitz operator; Bergman space; commutative C*-algebra; unit ball; Abelian groups of biholomorphisms; flat parallel submanifold; Lagrangian submanifold; Riemannian foliation; totally geodesic foliation;

D O I：

10.1007/s00020-007-1540-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the first part [16] of this work, we described the commutative C*- algebras generated by Toeplitz operators on the unit ball B-n whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of B-n. Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of the unit disk (see [3]) admits a natural generalization to the unit ball B-n. Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and "dynamic" properties of the level sets of generating symbols.

引用

页码：89 / 132

页数：44

共 37 条

[1] Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, II. Geometry of the Level Sets of Symbols
Raul Quiroga-Barranco
Nikolai Vasilevski
Integral Equations and Operator Theory, 2008, 60 : 89 - 132
[2] Commutative C*-Algebras Generated by Toeplitz Operators on the Super Unit Ball
R. Quiroga-Barranco
A. Sánchez-Nungaray
Advances in Applied Clifford Algebras, 2016, 26 : 363 - 397
[3] Commutative C*-Algebras Generated by Toeplitz Operators on the Super Unit Ball
Quiroga-Barranco, R.
Sanchez-Nungaray, A.
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2016, 26 (01) : 363 - 397
[4] Commutative C*-algebras of Toeplitz operators and quantization on the unit disk
Grudsky, S
Quiroga-Bartanco, R
Vasilevski, N
JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 234 (01) : 1 - 44
[5] Commutative C*-algebras of Toeplitz operators on the unit ball, I.: Bargmann-type transforms and spectral representations of Toeplitz operators
Quiroga-Barranco, Raul
Vasilevski, Nikolai
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 59 (03) : 379 - 419
[6] Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators
Raul Quiroga-Barranco
Nikolai Vasilevski
Integral Equations and Operator Theory, 2007, 59 : 379 - 419
[7] Toeplitz operators on the unit ball in Cn with radial symbols
Grudsky, S
Karapetyants, A
Vasilevski, N
JOURNAL OF OPERATOR THEORY, 2003, 49 (02) : 325 - 346
[8] Toeplitz Operators on the Unit Ball with Locally Integrable Symbols
Hagger, R.
Liu, C.
Taskinen, J.
Virtanen, J. A.
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2022, 94 (02)
[9] Toeplitz Operators on the Unit Ball with Locally Integrable Symbols
R. Hagger
C. Liu
J. Taskinen
J. A. Virtanen
Integral Equations and Operator Theory, 2022, 94
[10] Commutative Algebras Generated by Toeplitz Operators on the Unit Sphere
Maribel Loaiza
Nikolai Vasilevski
Integral Equations and Operator Theory, 2020, 92

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