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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  0;  1 and  2. Here we explicitly evaluate the Schur's function  3. Using this value wend necessary and sufficient conditions under which the Toeplitz operator T φ is hyponormal, where φ is a trigonometric polynomial given by φ( z ) = ∑N = N a n z n ( N 4) and satises the

ON HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL AND SYMMETRIC TYPE SYMBOLS