Compact linear combinations of composition operators induced by linear fractional maps

Boo Rim Choe; Hyungwoon Koo; Maofa Wang; Jongho Yang

doi:10.1007/s00209-015-1449-0

Compact linear combinations of composition operators induced by linear fractional maps

Boo Rim Choe, Hyungwoon Koo, Maofa Wang, Jongho Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.

Original language	English
Pages (from-to)	807-824
Number of pages	18
Journal	Mathematische Zeitschrift
Volume	280
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-015-1449-0
Publication status	Published - 2015 Aug 26

Keywords

Compact operator
Hardy space
Linear combination of composition operators
Linear fractional map
Weighted Bergman space

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-015-1449-0

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title = "Compact linear combinations of composition operators induced by linear fractional maps",

abstract = "It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.",

keywords = "Compact operator, Hardy space, Linear combination of composition operators, Linear fractional map, Weighted Bergman space",

author = "Choe, {Boo Rim} and Hyungwoon Koo and Maofa Wang and Jongho Yang",

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AU - Koo, Hyungwoon

AU - Wang, Maofa

AU - Yang, Jongho

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N2 - It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.

AB - It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and inducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension.

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KW - Hardy space

KW - Linear combination of composition operators

KW - Linear fractional map

KW - Weighted Bergman space

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Compact linear combinations of composition operators induced by linear fractional maps

Abstract

Keywords

ASJC Scopus subject areas

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