期刊论文

Lu, Yufeng

Lu, YF (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.

Shi, Yanyue

2009-09-01

INTEGRAL EQUATIONS AND OPERATOR THEORY

SCIE、Scopus

J

65

1

115-129

0378-620X

Hyponormality; weighted Bergman space; Hankel operator; Toeplitz operator

Consider phi - f + (g) over bar, where f and g are polynomials, and let T(phi) be the Toeplitz operators with the symbol phi. It is known that if T(phi) is hyponormal then vertical bar f'(z)broken vertical bar(2) >= vertical bar g'(z)vertical bar(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 T(phi) on the weighted Bergman space, which generalize the results of I. S. Hwang and J. Lee.