ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS

In [6], it was shown that hyponormality for Toeplitz operators with polynomial symbols can be reduced to classical Schur's algorithm in function theory. In [6], Zhu has also given the explicit values of the Schur's functions Phi(0), Phi(1) and Phi(2). Here we explicitly evaluate the Schur's function Phi(3). Using this value we find necessary and sufficient conditions under which the Toeplitz operator T(phi) is hyponormal, where phi is a trigonometric polynomial given by phi(z) = Sigma(N)(n=-N) a(n)z(n) (N >= 4) and satisfies the condition (a) over bar (N) (a-1 1-2 1-4 . . . a-N) = a-N ((a) over bar (1) ($) over bar (2) ($) over bar (3) . . . ($) over bar (N)). Finally we illustrate the easy applicability of the derived results with a few examples.