@article { ISI:000270281900003,
	title = {Connectedness of spectra of Toeplitz operators on Hardy spaces with Muckenhoupt weights over Carleson curves},
	journal = {Integral Equations and Operator Theory},
	volume = {65},
	number = {{1}},
	year = {2009},
	month = {{SEP}},
	pages = {83-114},
	publisher = {{BIRKHAUSER VERLAG AG}},
	type = {{Article}},
	address = {{VIADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND}},
	abstract = {<script src={\textquoteright}https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML{\textquoteright}></script><p>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 \(1 \&lt; p \&lt; \infty\). 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 \(H^p(\Gamma,w)\), \( 1 \&lt; p \&lt; \infty \), with general Muckenhoupt weights \(w\) over arbitrary Carleson curves \(\Gamma\). </p>
},
	keywords = {Carleson curve, essential spectrum, Hardy space, index, Muckenhoupt weight, Pettis integral}, spectrum, {Toeplitz operator},
	issn = {{0378-620X}},
	doi = {{10.1007/s00020-009-1710-1}},
	url = {http://www.springerlink.com/content/h278jp7j82518877/},
	author = {Karlovich, Alexei Yu. and Spitkovsky, Ilya M.}
}
