Some block Toeplitz composition operators

被引：2
作者：
Patton, Linda J. [1 ]
机构：
[1] Cal Poly, Dept Math, San Luis Obispo, CA 93407 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 400卷 / 02期
关键词：
Composition operator; Toeplitz operator; Numerical range; NUMERICAL RANGES;
D O I：
10.1016/j.jmaa.2012.11.057
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The composition operators on H-2(D) with minimal polynomial z(n) - 1 are shown to be block Toeplitz with Toeplitz symbol equal to an n x n matrix-valued polynomial of degree 1. This result is used to prove that the numerical range of a composition operator on H-2(D) with minimal polynomial z(3) - 1 cannot be a circular disk. (C) 2012 Elsevier Inc. All rights reserved.
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收藏
页码：363 / 376
页数：14
相关论文
共 28 条
[1]   The numerical range of a composition operator with conformal automorphism symbol [J].
Abdollahi, A .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 408 (1-3) :177-188
[2]   Numerical ranges of Toeplitz operators with matrix symbols [J].
Bebiano, Natalia ;
Spitkovsky, Ilya M. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (06) :1721-1726
[3]  
Bercovici H, 1988, Operator Theory and Arithmetic in H
[4]  
Bottcher A., 2006, SPRINGER MONOGRAPHS
[5]  
Bourdon P.S., 2002, INTEGR EQUAT OPER TH, V44, P401
[6]   The numerical ranges of automorphic composition operators [J].
Bourdon, PS ;
Shapiro, JH .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (02) :839-854
[7]  
Cowen C., 1995, Composition Operators on Spaces of Analytic Functions
[8]   LINEAR FRACTIONAL COMPOSITION OPERATORS ON H-2 [J].
COWEN, CC .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 1988, 11 (02) :151-160
[9]  
Gustafson KE., 1996, NUMERICAL RANGE FIEL
[10]  
Guyker J., 1989, ACTA SCI MATH SZEGED, V53, P369
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