Abstract.
Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space \(H^p({\mathbb{T}})\) over the unit circle \({\mathbb{T}}\) 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 \(H^2({\mathbb{T}})\). We show that, as was suspected, these results remain valid in the setting of Hardy spaces Hp(Γ,w), 1 < p < ∞, with general Muckenhoupt weights w over arbitrary Carleson curves Γ.
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The first author is partially supported by the grant FCT/FEDER/POCTI/MAT/59972/2004.
The second author is partially supported by NSF grant DMS-0456625.
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Karlovich, A.Y., Spitkovsky, I.M. Connectedness of Spectra of Toeplitz Operators on Hardy Spaces with Muckenhoupt Weights Over Carleson Curves. Integr. equ. oper. theory 65, 83–114 (2009). https://doi.org/10.1007/s00020-009-1710-1
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DOI: https://doi.org/10.1007/s00020-009-1710-1