Spectra of some weighted composition operators on H2

Carl C. Cowen, Eungil Ko, Derek Thompson, Feng Tian

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We completely characterize the spectrum of a weighted composition operator W Ψ,ℓ on H2(D) when ℓ has Denjoy-Wolff point a with 0 < |ℓ'′(α)| < 1, the iterates, ℓn, converge uniformly to a, and is in H∞ (the space of bounded analytic functions on D) and continuous at a. We also give bounds and some computations when |α| = 1 and ℓ'′(α) = 1 and, in addition, show that these symbols include all linear fractional ℓ that are hyperbolic and parabolic nonautomorphisms. Finally, we use these results to eliminate possible weights Ψ so that W Ψ,ℓ is seminormal.

Original languageEnglish
Pages (from-to)221-234
Number of pages14
JournalActa Scientiarum Mathematicarum
Volume82
Issue number1-2
DOIs
StatePublished - 2016

Keywords

  • Hyponormal operator
  • Spectrum of an operator
  • Weighted composition operator

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