Abstract
An operator T is asymptotic Toeplitz if for S the unilateral shift, the sequence S*nTS n converges. It is asymptotic Hankel if for J n the permutation isometry on the subspace determined by the first n coordinate vectors, the sequence J n TS n+1 converges. The relationship between these notions is studied and operator analogues of the A.A.K. distance formulae in terms of the s numbers of a Hankel operator are obtained.
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Dedicated to Professor Israel Gohberg on the occasion of his sixtieth birthday.
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© 1989 Birkhäuser Verlag Basel
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Feintuch, A. (1989). On Asymptotic Toeplitz and Hankel Operators. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 41. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9278-0_12
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DOI: https://doi.org/10.1007/978-3-0348-9278-0_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9975-8
Online ISBN: 978-3-0348-9278-0
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