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Estelle L. Basor and Torsten Ehrhardt
On a Class of Toeplitz + Hankel Operators
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| Published: |
March 3, 1999 |
| Keywords: |
Toeplitz operators, Hankel operators, Fredholm Index, Invertibility, Spectrum, Stability |
| Subject: |
47B35; secondary: 47A10, 47A35 |
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Abstract
In this paper we study operators of the form M(φ)=T(φ)+H(φ)
where T(φ) and H(φ) are the Toeplitz and Hankel operators
acting on l2.
We investigate the connection between Fredholmness and
invertibility of M(φ) for functions φ∈ L∞(T).
Using this relationship we establish necessary and sufficient
conditions for the invertibility of M(φ) with piecewise
continuous φ. Finally, we consider several stability problems
related to M(φ), in particular the stability of the finite
section method.
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| Acknowledgements
The first author was supported in part by NSF Grant DMS-9623278.
The second author was supported in part by DAAD Grant 213/402/537/5.
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| Author information
Estelle L. Basor:
Department of Mathematics,
California Polytechnic State University,
San Luis Obispo, CA 93407
ebasor@calpoly.edu
Torsten Ehrhardt:
Fakultät für Mathematik,
Technische Universität Chemnitz,
09107 Chemnitz, Germany
tehrhard@mathematik.tu-chemnitz.de
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