Complex symmetric Toeplitz operators on the weighted Bergman space

Eungil Ko, Ji Eun Lee, Jongrak Lee

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we give a characterization of a complex symmetric Toeplitz operator (Formula presented.) on the weighted Bergman space (Formula presented.). We first give properties of complex symmetric Toeplitz operators (Formula presented.) on (Formula presented.). Next, we prove that if (Formula presented.) is complex symmetric with finite symbol, then (Formula presented.) is hyponormal on (Formula presented.) if and only if it is hyponormal on the Hardy space (Formula presented.). Finally, we consider the complex symmetric Toeplitz operator (Formula presented.) on (Formula presented.) when the conjugation is a special case.

Original languageEnglish
Pages (from-to)1393-1408
Number of pages16
JournalComplex Variables and Elliptic Equations
Volume67
Issue number6
DOIs
StatePublished - 2022

Keywords

  • 47B15
  • Complex symmetric operator
  • Primary 47B35
  • Secondary 47A05
  • Toeplitz operator
  • normal operator
  • weighted Bergman space

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