The spectrum is discontinuous on the manifold of Toeplitz operators

A. Böttcher, S. Grudsky, I. Spitkovsky

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)46-52
Number of pages7
JournalArchiv der Mathematik
Volume75
Issue number1
DOIs
StatePublished - Jul 3 2000

ASJC Scopus subject areas

  • Mathematics(all)

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