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Absolute Values of Toeplitz Operators and Hankel Operators

Published online by Cambridge University Press:  20 November 2018

Takahiko Nakazi*
Affiliation:
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060, Japan
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Abstract

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Nehari's theorem for norms of bounded Hankel operators is revisited. Using it, the absolute values of Toeplitz operators are studied. This gives a theorem of Widom and Devinatz for invertible Toeplitz operators.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Cotlar, M. and Sadosky, C., On the Helson-Szego theorem and a related class of modified Toeplitz kernels, Proc. Symp. Pure Math. AMS 35:1 (1979), 383407.Google Scholar
2. Devinatz, A., Toeplitz operators on H2 spaces, Trans. Amer. Math. Soc. 112 (1964), 304317.Google Scholar
3. Douglas, R. G., Banach Algebra Techniques in Operator Theory, Academic Press, New York and London, 1972.Google Scholar
4. Douglas, R. G., On majorization, factorization, and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413416.Google Scholar
5. Garnett, J., Bounded Analytic Functions, Academic Press, New York, N.Y, 1981.Google Scholar
6. Koosis, P., Weighted quadratic means of Hilbert transforms, Duke Math. J. 38 (1971), 609634.Google Scholar
7. Nehari, Z., On bounded billinear forms, Ann. of Math. 65 (1957), 153162.Google Scholar
8. Power, S. C., Hankel Operators On Hilbert Space, Research Notes in Math. 64, Pitman Advanced Publishing Program, 1982.Google Scholar