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

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