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

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

18 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

Bibliographical note

Funding Information:
B. R. Choe was supported by NRF (2013R1A1A2004736) of Korea, H. Koo was supported by NRF (2012R1A1A2000705) of Korea and NSFC (11271293), and M. Wang was supported by NSFC (11271293).

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

Keywords

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00209-015-1449-0

Cite this

@article{663658f99faa4bc09702536b0b1f0125,

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",

note = "Funding Information: B. R. Choe was supported by NRF (2013R1A1A2004736) of Korea, H. Koo was supported by NRF (2012R1A1A2000705) of Korea and NSFC (11271293), and M. Wang was supported by NSFC (11271293). Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

year = "2015",

month = aug,

day = "26",

doi = "10.1007/s00209-015-1449-0",

language = "English",

volume = "280",

pages = "807--824",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - Compact linear combinations of composition operators induced by linear fractional maps

AU - Choe, Boo Rim

AU - Koo, Hyungwoon

AU - Wang, Maofa

AU - Yang, Jongho

N1 - Funding Information: B. R. Choe was supported by NRF (2013R1A1A2004736) of Korea, H. Koo was supported by NRF (2012R1A1A2000705) of Korea and NSFC (11271293), and M. Wang was supported by NSFC (11271293). Publisher Copyright: © 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/8/26

Y1 - 2015/8/26

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.

KW - Compact operator

KW - Hardy space

KW - Linear combination of composition operators

KW - Linear fractional map

KW - Weighted Bergman space

UR - http://www.scopus.com/inward/record.url?scp=84937975139&partnerID=8YFLogxK

U2 - 10.1007/s00209-015-1449-0

DO - 10.1007/s00209-015-1449-0

M3 - Article

AN - SCOPUS:84937975139

SN - 0025-5874

VL - 280

SP - 807

EP - 824

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Compact linear combinations of composition operators induced by linear fractional maps

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this