Complex symmetric composition operators on weighted Hardy spaces

Sivaram K. Narayan, Daniel Sievewright, Maria Tjani

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let ϕ be an analytic self-map of the open unit disk D. We study the complex symmetry of composition operators Cϕ on weighted Hardy spaces induced by a bounded sequence. For any analytic self-map of D that is not an elliptic automorphism, we establish that if Cϕ is complex symmetric, then either ϕ(0) = 0 or ϕ is linear. In the case of weighted Bergman spaces A2 α, we find the non-automorphic linear fractional symbols ϕ such that Cϕ is complex symmetric.

Original languageEnglish
Pages (from-to)2117-2127
Number of pages11
JournalProceedings of the American Mathematical Society
Volume148
Issue number5
DOIs
StatePublished - 2020

Keywords

  • Complex symmetric operator
  • Composition operator
  • Conjugation
  • Linear fractional maps
  • Weighted Bergman space
  • Weighted Hardy space

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