On Hyponormal Toeplitz Operators with Trigonometric Polynomial Symbols

Authors

  • Ambeswar Phukon Department of Mathematics, Kokrajhar Government College, Kokrajhar 783370, Assam

DOI:

https://doi.org/10.26713/cma.v6i2.317

Keywords:

Toeplitz operators, Hyponormal operators, Trigonometric polynomial, Symmetry

Abstract

This paper gives a necessary and sufficient conditions for the hyponormality of a Toeplitz operator \(T_\varphi\) on the trigonometric polynomial symbol of the type \(\varphi(z)=\sum_{n=-N}^Na_nz^n\) under some certain assumptions of the Fourier coefficients of \(\varphi\).

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References

A. Böttcher and B.C. Silbermann, Analysis of Teoplitz Operators, Springer Verlag, New York, (1990).

C.C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), 809–812.

R.E. Curto and W.Y. Lee, Joint hyponormality of Toeplitz pairs, Memoirs of Amer. Math. Soc. 150 (712) (2001), Amer. Math. Soc., Providence.

D.R. Farenick and W.Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc., 348 (1996), 4153–4174.

M. Hazarika and A. Phukon, On hyponormality of Toeplitz operators with polynomial and symmetrictype symbols, Bull. Korean Math. Soc. 48 (2011), 617–625.

M. Hazarika and A. Phukon, On hyponormality of trigonometric Toeplitz operators, Internat. J. Functional Analysis, Operator Theory and Applications 3 (2011), 163–189.

I.S. Hwang and W.Y. Lee, Hyponormality of Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations Operator Theory 50 (2004), 363–373.

I.H. Kim and W.Y. Lee, On hyponormal Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations Operator Theory 32 (1998), 216–233.

T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338 (1993), 753–767.

K. Zhu, Hyponormal Toeplitz operators with polynomial symbolsv, Integral Equations Operator Theory 21 (1995), 376–381.

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Published

25-12-2015
CITATION

How to Cite

Phukon, A. (2015). On Hyponormal Toeplitz Operators with Trigonometric Polynomial Symbols. Communications in Mathematics and Applications, 6(2), 49–54. https://doi.org/10.26713/cma.v6i2.317

Issue

Section

Research Article