### 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 H^{2}(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 | |

State | Published - Sep 1 2009 |

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### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

*65*(1), 83-114. https://doi.org/10.1007/s00020-009-1710-1

**Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves.** / Karlovich, Alexei Yu; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 65, no. 1, pp. 83-114. https://doi.org/10.1007/s00020-009-1710-1

}

TY - JOUR

T1 - Connectedness of spectra of toeplitz operators on hardy spaces with muckenhoupt weights over carleson curves

AU - Karlovich, Alexei Yu

AU - Spitkovsky, Ilya

PY - 2009/9/1

Y1 - 2009/9/1

N2 - 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

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

UR - http://www.scopus.com/inward/record.url?scp=71749085021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71749085021&partnerID=8YFLogxK

U2 - 10.1007/s00020-009-1710-1

DO - 10.1007/s00020-009-1710-1

M3 - Article

VL - 65

SP - 83

EP - 114

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -