Compact Differences of Composition Operators in Several Variables

被引：22

作者：

Heller, Katherine ^{[1
]}

MacCluer, Barbara D. ^{[1
]}

Weir, Rachel J. ^{[2
]}

机构：

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[2] Allegheny Coll, Dept Math, Meadville, PA 16335 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2011年 / 69卷 / 02期

关键词：

TOEPLITZ;

D O I：

10.1007/s00020-010-1840-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When phi and psi are linear-fractional self-maps of the unit ball B-N in C-N, N >= 1, we show that the difference C phi-C psi cannot be non-trivially compact on either the Hardy space H-2(B-N) or any weighted Bergman space A(alpha)(2)(B-N). Our arguments emphasize geometrical properties of the inducing maps phi and psi.

引用

页码：247 / 268

页数：22

共 15 条

[1]

[Anonymous], COMPOSITION OPERATOR

[2]

[Anonymous], COMPACT DIFFERENCES

[3]

[Anonymous], COMPOSITION OPERATOR

[4]

[Anonymous], FUNCTION THEORY UNIT

[5]

[Anonymous], ISRAEL J MA IN PRESS

[6] Components of linear-fractional composition operators [J].

Bourdon, PS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 279 (01) :228-245

[7] Classification of semigroups of linear fractional maps in the unit ball [J].

Bracci, Filippo ;

Contreras, Manuel D. ;

Diaz-Madrigal, Santiago .

ADVANCES IN MATHEMATICS, 2007, 208 (01) :318-350

[8]

Cowen CC., 2000, ACTA SCI MATH SZEGED, V66, P351

[9] C*-algebras generated by groups of composition operators [J].

Jury, Michael T. .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (06) :3171-3192

[10] The Fredholm index for elements of Toeplitz-composition C*-algebras [J].

Jury, Michael T. .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 58 (03) :341-362

← 1 2 →