Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves

Alexei Yu Karlovich, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review

Abstract

Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space Hp(T) over the unit circle T is a connected subset of the complex plane for every bounded measurable symbol a and 1 < p < ∞. In 1972, Ronald Douglas established the connectedness of the essential spectrum of T(a) on H2(T). We show that, as was suspected, these results remain valid in the setting of Hardy spaces Hp(G,&ohgr;),1<p<∞, with general Muckenhoupt weights &ohgr; over arbitrary Carleson curves G.

Original languageEnglish (US)
Pages (from-to)83-114
Number of pages32
JournalIntegral Equations and Operator Theory
Volume65
Issue number1
DOIs
StatePublished - Sep 2009

Keywords

  • Carleson curve
  • Essential spectrum
  • Hardy space
  • Index
  • Muckenhoupt weight
  • Pettis integral
  • Spectrum
  • Toeplitz operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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