Abstract
The essential spectra of Toeplitz operators with piecewise continuous and almost periodic symbols admit pretty nice geometric descriptions. In contrast to this, little is known about the essential spectra of Toeplitz operators with semi-almost periodic symbols, that is, with symbols belonging to the algebra generated by the continuous functions on the real line with a jump at infinity and by the continuous almost periodic functions. A classical result by Sarason enables us to decide whether the Toeplitz operatorT(a-λ) is Fredholm for a given point a in the plane, but the problem of characterizing the set ofallλ for whichT(a -λ) is not Fredholm is nevertheless intricate. This question is studied in the present paper.
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References
A. Böttcher, S. Grudsky, and I. Spitkovsky: The spectrum is discontinuous on the manifold of Toeplitz operators.Arch. Math.75 (2000), 46–52.
A. Böttcher and B. Silbermann:Analysis of Toeplitz Operators.Akademie-Verlag, Berlin 1989 and Springer-Verlag, Berlin, Heidelberg, New York 1990.
L.A. Coburn and R.G. Douglas: Translation operators on a half-line.Proc. Nat. Acad. Sci. USA62 (1969), 1010–1013.
R.G. Douglas:Banach Algebra Techniques in Operator Theory. Academic Press, New York 1972; 2nd edition: Springer-Verlag, New York 1998.
D.R. Farenick and W.Y. Lee: Hyponormality and spectra of Toeplitz operators.Trans. Amer. Math. Soc.348 (1996), 4153–4174.
I. Gohberg and I.A. Feldman: On Wiener-Hopf integro-difference equations.Soviet Math. Dokl.9 (1968), 1312–1316.
S. Hwang and W.Y. Lee: On the continuity of spectra of Toeplitz operators.Arch. Math.70 (1998), 66–73.
N.K. Nikolski:Treatise on the shift operator.Springer-Verlag, Berlin, Heidelberg, New York 1986.
D. Sarason: Toeplitz operators with semi-almost periodic symbols.Duke Math. J.44 (1977), 357–364.
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Böttcher, A., Grudsky, S., Spitkovsky, I. (2003). On the Essential Spectrum of Toeplitz Operators with Semi-Almost Periodic Symbols. In: Böttcher, A., Kaashoek, M.A., Lebre, A.B., dos Santos, A.F., Speck, FO. (eds) Singular Integral Operators, Factorization and Applications. Operator Theory: Advances and Applications, vol 142. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8007-7_3
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DOI: https://doi.org/10.1007/978-3-0348-8007-7_3
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