Normal and cohyponormal weighted composition operators on H2

Carl C. Cowen, Sungeun Jung, Eungil Ko

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this paper we study normal and cohyponormal weighted composition operators on the Hardy space H2. We show that if Wf,ᵠ is cohyponormal, then f is outer and ϕ is univalent. Moreover, we prove that when the composition map ᵠ has the Denjoy-Wolff point in the open unit disk, Wf,ᵠ is cohyponormal if and only if it is normal; in this case, f and ᵠ can be expressed as linear fractional maps. As a corollary, we find the polar decomposition of the cohyponormal operator Wf,ᵠ. Finally, we examine the commutant of a cohyponormal weighted composition operator.

Original languageEnglish
Pages (from-to)69-85
Number of pages17
JournalOperator Theory: Advances and Applications
Volume240
DOIs
StatePublished - 2014

Keywords

  • Cohyponormal operator
  • Commutant
  • Composition operator
  • Hyponormal operator
  • Inner-outer factorization
  • Normal operator
  • Polar decomposition
  • Weighted composition operator

Fingerprint

Dive into the research topics of 'Normal and cohyponormal weighted composition operators on H2'. Together they form a unique fingerprint.

Cite this