Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-09-01

Journal: INTEGRAL EQUATIONS AND OPERATOR THEORY

Included Journals: Scopus、SCIE

Volume: 65

Issue: 1

Page Number: 115-129

ISSN: 0378-620X

Key Words: Hyponormality; weighted Bergman space; Hankel operator; Toeplitz operator

Abstract: 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.