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

Alexei Yu Karlovich; Ilya M. Spitkovsky

doi:10.1007/s00020-009-1710-1

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

Alexei Yu Karlovich, Ilya M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space H^p(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 H^p(G,&ohgr;),1<p<∞, with general Muckenhoupt weights &ohgr; over arbitrary Carleson curves G.

Original language	English (US)
Pages (from-to)	83-114
Number of pages	32
Journal	Integral Equations and Operator Theory
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/s00020-009-1710-1
State	Published - 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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10.1007/s00020-009-1710-1

Cite this

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title = "Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves",

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",

keywords = "Carleson curve, Essential spectrum, Hardy space, Index, Muckenhoupt weight, Pettis integral, Spectrum, Toeplitz operator",

author = "Karlovich, {Alexei Yu} and Spitkovsky, {Ilya M.}",

note = "Funding Information: 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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doi = "10.1007/s00020-009-1710-1",

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AU - Karlovich, Alexei Yu

AU - Spitkovsky, Ilya M.

N1 - Funding Information: 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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AB - 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

KW - Carleson curve

KW - Essential spectrum

KW - Hardy space

KW - Index

KW - Muckenhoupt weight

KW - Pettis integral

KW - Spectrum

KW - Toeplitz operator

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

Abstract

Keywords

ASJC Scopus subject areas

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