Compact linear combinations of composition operators induced by linear fractional maps

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

Research output: Contribution to journalArticlepeer-review

17 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 languageEnglish
Pages (from-to)807-824
Number of pages18
JournalMathematische Zeitschrift
Volume280
Issue number3-4
DOIs
Publication statusPublished - 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

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