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On Asymptotic Toeplitz and Hankel Operators

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The Gohberg Anniversary Collection

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 40/41))

Abstract

An operator T is asymptotic Toeplitz if for S the unilateral shift, the sequence {S ✹n n TS n} converges. It is asymptotic Hankel if for J n the permutation insometry 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 40/41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9144-8_29

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  • DOI: https://doi.org/10.1007/978-3-0348-9144-8_29

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9924-6

  • Online ISBN: 978-3-0348-9144-8

  • eBook Packages: Springer Book Archive

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