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

Alexei Yu Karlovich, Ilya Spitkovsky

Research output: Contribution to journalArticle

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 1 2009

Fingerprint

Muckenhoupt Weights
Toeplitz Operator
Connectedness
Hardy Space
Curve
Essential Spectrum
Unit circle
Argand diagram
Valid
Subset
Arbitrary

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

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

In: Integral Equations and Operator Theory, Vol. 65, No. 1, 01.09.2009, p. 83-114.

Research output: Contribution to journalArticle

@article{eaa50fe1ccb44158a9489bfa9c46d2ac,
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 Ilya Spitkovsky",
year = "2009",
month = "9",
day = "1",
doi = "10.1007/s00020-009-1710-1",
language = "English (US)",
volume = "65",
pages = "83--114",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkhauser Verlag Basel",
number = "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

AN - SCOPUS:71749085021

VL - 65

SP - 83

EP - 114

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -