@article{99a62f66c1444284893ebb4269cc484b,
title = "The spectrum is discontinuous on the manifold of Toeplitz operators",
abstract = "We answer in the negative a question by Farenick and Lee as to whether or not the spectrum is a continuous set-valued function on the linear space of Toeplitz operators. Thus, we show that if {an} is any sequence of the functions which converge uniformly to a function a ∈ L∞, then the spectra of the Toeplitz operators T(an) need not converge to the spectrum of the Toeplitz operator T(a) in the Hausdorff metric. The counterexample is constructed with semi-almost periodic functions an and a.",
author = "A. B{\"o}ttcher and S. Grudsky and I. Spitkovsky",
note = "Funding Information: Acknowledgements. The research of B{\"o}ttcher and Grudsky into this topic was essentially supported by DFG-Kooperationsprojekt 436 RUS 113/426 for German and Russian scientists within the “Memorandum of Understanding” beween DFG and RFFI. B{\"o}ttcher and Spitkovsky also acknowledge support by NATO Collaborative Research Grant CRG 950332, Grudsky also acknowledges support by RFFI Grant 98-01-01023, and Spitkovsky also acknowledges support by NSF Grant 9800704.",
year = "2000",
month = jul,
day = "3",
doi = "10.1007/s000130050472",
language = "English (US)",
volume = "75",
pages = "46--52",
journal = "Archiv der Mathematik",
issn = "0003-889X",
publisher = "Birkhauser Verlag Basel",
number = "1",
}