Complex symmetric weighted composition operators on H2(D)

Sungeun Jung, Yoenha Kim, Eungil Ko, Ji Eun Lee

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

In this paper we study complex symmetric weighted composition operators on the Hardy space. We provide some characterizations of ψ and φ when a weighted composition operator Wψ,φ is complex symmetric. We investigate which combinations of weights ψ and maps of the open unit disk φ give rise to complex symmetric weighted composition operators with a special conjugation. As some applications, we obtain several examples for nonnormal complex symmetric operators. In addition, we give spectral properties of complex symmetric weighted composition operators. We examine eigenvalues and eigenvectors of such operators and find some conditions for which a complex symmetric weighted composition operator is Hilbert-Schmidt. Finally, we consider cyclicity, hypercyclicity, and the single-valued extension property for complex symmetric weighted composition operators.

Original languageEnglish
Pages (from-to)323-351
Number of pages29
JournalJournal of Functional Analysis
Volume267
Issue number2
DOIs
StatePublished - 15 Jul 2014

Keywords

  • Complex symmetric
  • Hilbert-Schmidt
  • The single-valued extension property
  • Weighted composition operator

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