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Hyponormal Toeplitz Operators on the Weighted Bergman Space
Authors:Yufeng Lu  Yanyue Shi
Institution:1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
Abstract:Consider j = f +`(g)]\varphi = f + \overline {g}, where f and g are polynomials, and let TjT_{\varphi} be the Toeplitz operators with the symbol j\varphi. It is known that if TjT_{\varphi} is hyponormal then |f¢(z)|2 3 |g¢(z)|2|f'(z)|^{2} \geq |g'(z)|^{2} on the unit circle in the complex plane. In this paper, we show that it is also a necessary and sufficient condition under certain assumptions. Furthermore, we present some necessary conditions for the hyponormality of TjT_{\varphi} on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee.
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