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THE FINITE SUM OF THE PRODUCTS OF TWO TOEPLITZ OPERATORS

Part of: Special classes of linear operators

Published online by Cambridge University Press:  01 February 2009

XUANHAO DING
XUANHAO DING*
Affiliation:
College of Science, Chong Qing Technology and Business University, Chong Qing, 400067, PR China (email: [email protected])
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Abstract

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We consider in this paper the question of when the finite sum of products of two Toeplitz operators is a finite-rank perturbation of a single Toeplitz operator on the Hardy space over the unit disk. A necessary condition is found. As a consequence we obtain a necessary and sufficient condition for the product of three Toeplitz operators to be a finite-rank perturbation of a single Toeplitz operator.

Keywords

Hardy spaceToeplitz operatorsfinite-rank operators

MSC classification

Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 1 , February 2009 , pp. 45 - 60
Copyright
Copyright © Australian Mathematical Society 2009

References

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