Subnormality and composition operators on the Bergman space

被引：6

作者：

Richman, AE ^{[1
]}

机构：

[1] Purdue Univ, W Lafayette, IN 47905 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2003年 / 45卷 / 01期

关键词：

47B33; 47B32; 47B20;

D O I：

10.1007/BF02789595

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Following the work of C. Cowen and T. Kriete on the Hardy space, we prove that under a regularity condition, all composition operators with a subnormal adjoint on A(2)(D) have linear fractional symbols of the form phi(z) = ((r+s)z+(1-s)d)/(r(1-s)(d) over barz+(1+sr)) Moreover, we show that all composition operators on the Bergman space having these symbols have a subnormal adjoint, with larger range for the parameter r than found in the Hardy space case.

引用

页码：105 / 124

页数：20

共 24 条

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BAKER IN, 1979, J LOND MATH SOC, V20, P255

[2]

Conway J. B., 1991, The theory of subnormal operators

[3]

COWEN C., 1995, Studies in Advanced Mathematics

[4] SUBNORMALITY AND COMPOSITION OPERATORS ON H-2 [J].