COMPACT DIFFERENCE OF COMPOSITION OPERATORS ON THE HARDY SPACES

Boo Rim Choe, Koeun Choi, Hyungwoon Koo, Inyoung Park

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Answering to a long-standing question raised by Shapiro and Sundberg in 1990, Choe et al. have recently obtained a characterization for compact differences of composition operators acting on the Hilbert-Hardy space over the unit disk. Their characterization is described in terms of cer-tain Bergman-Carleson measures involving derivatives of the inducing maps. In this paper, based on such results, we take one step further to obtain a completely new characterization, which is more intuitive and much simpler. In particular, our new characterization does not involve derivatives of the inducing maps and includes the Reproducing Kernel Thesis characterization. Moreover, our proofs are constructive enough to yield optimal estimates for the essential norms.

Original languageEnglish
Pages (from-to)733-756
Number of pages24
JournalTransactions of the American Mathematical Society Series B
Volume9
Issue number24
DOIs
Publication statusPublished - 2022

Bibliographical note

Funding Information:
Received by the editors June 5, 2022. 2020 Mathematics Subject Classification. Primary 47B33; Secondary 30H10, 30H20. Key words and phrases. Difference of composition operator, compactness, Hardy space, bounded multiplicity. The first author was supported by NRF (2018R1D1A1B07041183) of Korea, the third author was supported by NRF (2022R1F1A1063305) of Korea and the fourth author was supported by NRF (2021R1I1A1A01047051) of Korea and NRF (2020R1A4A3079066) of the Ministry of Science and ICT of Korea.

Publisher Copyright:
© 2022 by the author(s).

Keywords

  • Difference of composition operator
  • Hardy space
  • bounded multiplicity
  • compactness

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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