Bergman space structure, commutative algebras of toeplitz operators, and hyperbolic geometry

被引：25

作者：

Vasilevski, NL ^{[1
]}

机构：

[1] Inst Politecn Nacl, CINVESTAV, Dept Matemat, Mexico City 07000, DF, Mexico

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2003年 / 46卷 / 02期

关键词：

Toeplitz operators; Bergman space; hyperbolic geometry;

D O I：

10.1007/s000200300026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We exhibit a surprising but natural connection among the Bergman space structure, commutative algebras of Toeplitz operators and pencils of hyperbolic straight lines. The commutative C*-algebras of Toeplitz operators on the unit disk can be classified as follows. Each pencil of hyperbolic straight lines determines the set of symbols consisting of functions which are constant on corresponding cycles, the orthogonal trajectories to lines forming a pencil. It turns out that the C*-algebra generated by Toeplitz operators with this class of symbols is commutative.

引用

页码：235 / 251

页数：17

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