ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS

Title & Authors
ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS
Hazarika, Munmun; Phukon, Ambeswar;

Abstract
In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schurs algorithm in function theory. In [6], Zhu has also given the explicit values of the Schurs functions $\small{{\Phi}_0}$, $\small{{\Phi}_1}$ and $\small{{\Phi}_2}$. Here we explicitly evaluate the Schur`s function $\small{{\Phi}_3}$. Using this value we find necessary and sufficient conditions under which the Toeplitz operator $\small{T_{\varphi}}$ is hyponormal, where $\small{{\varphi}}$ is a trigonometric polynomial given by $\small{{\varphi}(z)}$
Keywords
Toeplitz operators;hyponormal operators;trigonometric poly-nomial;
Language
English
Cited by
References
1.
C. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), no. 3, 809-812.

2.
D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no. 10, 4153-4174.

3.
I. S. Hwang and W. Y. Lee, Hyponormality of Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations Operator Theory 50 (2004), no. 3, 363-373.

4.
T. Ito and T. K. Wong, Subnormality and quasinormality of Toeplitz operators, Proc. Amer. Math. Soc. 34 (1972), 157-164.

5.
I. H. Kim and W. Y. Lee, On hyponormal Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations Operator Theory 32 (1998), no. 2, 216-233.

6.
K. Zhu, Hyponormal Toeplitz operators with polynomial symbols, Integral Equations Operator Theory 21 (1995), no. 3, 376-381.

7.
Wolfram Research, Inc. Mathematica, Version 5.1, Wolfram Research, Inc., Champaign, IL, 1996.