Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea ; Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Abstract:
In this paper we establish a tractable and explicit criterion for the hyponormality of arbitrary trigonometric Toeplitz operators, i.e., Toeplitz operators with trigonometric polynomial symbols . Our criterion involves the zeros of an analytic polynomial induced by the Fourier coefficients of . Moreover the rank of the selfcommutator of is computed from the number of zeros of in the open unit disk and in counting multiplicity.